oninr  OF 

the  estate  of 
Professor  William  F.  Meyer 


TABLES  OF  LOGARITHMS 


TO 


FIVE  PLACES  OF  DECIMALS, 


WITH   AUXILIARY   TABLES. 


EDITED  BY 

EDWIN   S.  CRAWLEY,  PH.D., 

-       THOMAS  A.  SCOTT  PROFESSOR  OF  MATHEMATICS  IN  THE  UNIVERSITY  OF  PENNSYLVANIA 


E.  S.  CRAWLEY, 

UNIVERSITY   OF   PENNSYLVANIA, 

PHILADELPHIA, 

1905. 


COPYRIGHT,  1890, 

BY 
EDWIN  S.  CRAWLKY. 


ELECTROTVPEO  AND  PHINTED  BY  J.  B.  LIPPINCOTT  COMPANY,  PHILADELPHIA.  U.S.  A 


EDITOR'S  NOTE. 


THIS  collection  of  logarithmic  tables  has  been  prepared  to 
accompany  the  editor's  Elements  of  Trigonometry^  in  response 
to  the  demand  of  a  number  of  teachers  using  the  latter,  who 
prefer  a  text  bound  with  tables.  In  commending  the  tables 
to  the  use  of  educational  institutions  and  the  mathematical 
public  in  general,  the  editor  wishes  to  state  that  great  care  has 
been  taken  to  secure  accuracy.  The  proof  has  been  com- 
pared twice,  number  by  number,  with  different  standard  tables 
(Yega's  seven-place  Tables,  the  74th  edition,  edited  by  W.  L. 
F.  Fischer;  and  Gauss's  five-place  Tables,  the  20th  edition), 
and  the  method  of  differences  was  applied  as  a  further  check. 
Besides  these,  other  tests  were  applied  to  parts  of  the  tables, 
as  in  the  case  of  Table  III.,  where  the  log  tan  column  was 
checked  by  taking  the  difference  of  log  sin  and  log  cos,  and 
the  log  cot  column  was  checked  by  taking  the  arithmetical 
complement  of  log  tan. 

Should  any  errors  be  discovered,  the  editor  will  be  glad  to 
be  informed  of  them. 

EDWIN  S.  CKAWLEY. 

UNIVERSITY  OF  PENNSYLVANIA, 
January,  1899. 


C8 


M577188 


TABLE  OF  CONTENTS. 


EXPLANATION  or  THE  TABLES vii 

TABLE         I. — Logarithms  of  Numbers 1 

"  II.— Important  Constants  and  their  Logarithms 20 

"  III.— Logarithms  of  the  Sine,  Cosine,  Tangent,  Cotangent 

for  every  Minute  of  the  Quadrant 21 

"  IV.— Table  for  Computing  the  Log  Sin  and  Log  Tan  of 

Small  Angles 67 

"  V. — Natural  Sines,  Cosines,  Tangents,  and  Cotangents  .  .  69 

"  VI. — Circular  Arcs,  expressed  in  Kadians 74 

*•  VII. — Napierian  Logarithms  of  Numbers 75 


EXPLANATION  OF  THE  TABLES. 


1.  Definitions  and  Rules.  If  three  numbers  n,  a,  x  have 
such  values  that  the  equation 

n  =  a*  (1) 

is  true,  then  x  is  called  the  logarithm  of  n  to  the  base  a.  If, 
without  changing  a,  we  give  to  n  and  x  all  possible  values,  con- 
sistent with  this  equation,  the  values  of  x  thus  obtained  form 
a  system  of  logarithms  to  the  base  a. 

Hence : — The  logarithm  of  a  number  to  a  given  base  is  the  ex- 
ponent of  the  power  to  which  the  base  must  be  raised  to  produce  the 
number. 

Suppose  9  is  taken  for  the  base,  then 

log  81  =  2,  because  92  =  81 
11  729=  3,  "  93  =729 
«  i  =  -l,  -"  9~!=  i 
"  3=  i,  «  9*  =  3 
"  9=  1,  "  91  =  9 
"  1=  0,  "  9°  =  1 

In  every  system  the  logarithm  of  the  base  is  1,  and  the 
logarithm  of  1  is  0.  This  follows  directly  from  the  definition, 
or  from  (1)  ;  for  if  n  =  a,  x  must  be  1 ;  and  if  n  =  1,  x  must 
be  0,  without  respect  to  the  value  of  a. 

It  is  plain,  since  any  number  will  serve  as  the  base  of  a 
system  of  logarithms,  that  the  number  of  such  systems  is 
indefinite. 

vii 


Vlll  EXPLANATION   OF   THE   TABLES. 

The  systems  of  logarithms  commonly  used  are  : 

(1.)  The  common  or  Briggian*  system,  with  the  base  10. 

(2.)  The  natural  or  Napierianf  system  with  the  base 

6  =  2.7182818285  ____ 
defined  by  the  convergent  infinite  series 

e=1  +  1  +  r2  +  ii3+i^-4  +  --- 

Of  these  two  systems,  the  first  is  used  for  all  purposes  of 
numerical  computation,  and  the  second  for  purely  analytical 
purposes. 

The  logarithms  of  these  tables  (except  in  Table  VII.)  are 
common  or  Briggian  logarithms. 

The  corresponding  logarithms  of  any  two  systems  are  in  a 
constant  ratio  to  each  other.  Thus  the  relation  between  com- 
mon and  Napierian  logarithms  is 


(This  equation  is  read  :  "  Logarithm  of  n  to  the  base  10  equals 
the  reciprocal  of  the  logarithm  of  10  to  the  base  e,  multiplied 

bv  the  logarithm  of  n  to  the  base  e.")     The  factor  -  is 

log  .  10 

called  the  modulus  of  the  common  system.     It  is  represented 
by  M,  and  its  value  to  ten  places  is  0.4342944819. 

The  rules  governing  the  use  of  logarithms  in  computation 
are  the  following  :  — 

I.  To  multiply  numbers,  find  the  logarithm  of  each  factor,  and 
add  them  ;  the  sum  is  the  logarithm  of  the  product. 

II.  To  divide  one  number  by  another,  subtract  the  logarithm 
of  the  divisor  from  the  logarithm  of  the  dividend  ;  the  difference  is 
the  logarithm  of  the  quotient. 

III.  To  raise  a  number  to  any  power  multiply  the  logarithm  of 
the  number  by  the  exponent  of  the  power  ;  the  product  is  the  log- 
arithm of  the  required  power  of  the  number. 

*  Named  for  Henry  Briggs  (1666-1631),  who  first  suggested  the  use  of 
the  base  10. 

f  Named  for  John  Napier,  Baron  of  Merchiston,  in  Scotland  (1560- 
1617),  the  inventor  of  logarithms. 


EXPLANATION  OF  THE  TABLES.  IX 

IY.  To  extract  any  root  of  a  number,  divide  the  logarithm  of 
the  number  by  the  index  of  the  root ;  the  quotient  is  the  logarithm 
of  the  required  root  of  the  number. 

These  statements  and  rules  .are  given  without  proof,  as  the 
purpose  here  is  simply  to  familiarize  the  student  with  the 
mechanism  and  use  of  the  tables.  The  theory  of  logarithms 
is  set  forth  in  text-books  on  algebra,  to  which  the  student  is 
referred.  In  the  same  place  will  be  found  an  explanation  of 
how  logarithms  are  computed. 


TABLE  I.     Common  Logarithms  of  Numbers.    (Pages  1-19) 

2.  Characteristic  and  Mantissa.  A  logarithm  consists, 
usually,  of  two  parts :  a  whole  number,  called  the  characteristic, 
and  an  incommensurable  decimal  fraction,  called  the  mantissa. 
The  table  gives  only  the  mantissa ;  the  characteristic,  which 
may  be  positive,  negative,  or  zero,  must  be  supplied  in  every 
case  by  the  computer.  The  mantissa  is  always  positive,  ex- 
cept in  the  logarithms  of  exact  powers  of  10,  when  it  is  zero. 

Since  10  is  the  base  we  have : 


log  100Q  =     3,  because  103     =  1000 

log   100=     2,  "  102     =   100 

log     10=     If  "  10l     =     10 

log       1=     0,  "  10°     =       1 

log      a  =  — 1,  "  10  ~l  =      .1 

log    .01=— 2,  "  10-2=    .01 

log  .001  =  —3,  "  10  ~3  =  .001 


(a) 


This  series  of  equations  can  be  extended  indefinitely  in  both 
directions. 

Let  us  now  consider  two  numbers  which  contain  the  same 
sequence  of  figures,  with  different  positions  of  the  decimal 
point,  say  72.936  and  .72936.  Now  72.936  =  100  X  .72936. 
Hence,  by  Eule  I,  §  1  log  72.936  =  log  100  -f  log  .72936, 

or,  by  (a)  =  2  +  log  .72936. 

Hence,  since  any  change  in  the  position  of  the  decimal 


X  EXPLANATION   OF   THE   TABLES. 

point  in  a  number  is  equivalent  to  multiplication  or  division 
by  a  power  of  10,  the  effect  produced  upon  the  logarithm  of 
the  number  by  a  change  of  this  kind  is  to  increase  it  or 
diminish  it  by  a  whole  number ;  that  is,  the  characteristic  is 
affected  by  such  a  change,  but  not  the  mantissa.  We  have, 
therefore,  the  following  important  fact : 

I.  The  mantissa  of  the  logarithm  of  a  number  depends  only 
upon  the  sequence  of  figures  in  the  number. 

Referring  again  to  (a),  we  note  that  for  all  numbers  greater 
than  1  and  less  than  10  (all  numbers  with  one  significant 
figure  before  the  decimal  point)  the  logarithm  is  greater  than 
0  and  less  than  1,  that  is,  its  characteristic  is  0 ;  for  all  num- 
bers greater  than  10  and  less  than  100  (all  numbers  with  two 
significant  figures  before  the  decimal  point)  the  logarithm  is 
greater  than  1  and  less  than  2,  that  is,  its  characteristic  is  1 ; 
for  all  numbers  greater  than  100  and  less  than  1000  (all -num- 
bers with  three  significant  figures  before  the  decimal  point) 
the  logarithm  is  greater  than  2  and  less  than  3,  that  is,  its 
characteristic  is  2;  and  so  on.  Hence,  we  have  the  following 
rule: 

II.  The  characteristic  of  the  logarithm  of  a  number  greater  than 
unity  is  one  less  than  the  number  of  significant  figures  preceding 
the  decimal  point. 

Again,  from  (#)  it  will  be  seen  that  if  a  number  is  greater 
than  .1  and  less  than  1,  its  logarithm  is  between  0  and  — 1  ; 
that  is,  using  a  positive  mantissa,  which  we  always  do,  it  is 
— 1  -f  the  mantissa,  hence  the  characteristic  is  — 1 ;  if  the 
number  is  greater  than  .01  and  less  than  .1,  the  logarithm  is 
between  — 1  and  — 2,  which  is  written  — 2  -f-  the  mantissa, 
that  is,  the  characteristic  is  — 2  ;  if  the  number  is  greater  than 
.001  and  less  than  .01,  the  logarithm  is  between  — 2  and  — 3, 
which  is  written  — 3  -f-  the  mantissa,  that  is,  the  characteristic 
is  — 3,  and  so  on.  Hence,  we  have  the  following  rule : 

III.  The  characteristic  of  the  logarithm  of  a  number  less  than 
unity  is  negative,  and  is  numerically  one  greater  than  the  number 
of  ciphers  between  the  decimal  point  and  the  first  significant 
figure. 


EXPLANATION   OF  THE   TABLES.  XI 

Verify  the  following  statements : 

characteristic  of  log  763.92  =     2 

"  "  log  1.9841—     0 

*'  "log  .07296  =  — 2 

"  "  log  26        =     1 

"  "  log  400000=     5 

"  "  log  .9426  =  —! 

"  "   log  3869=     3 

"  "  log  .00042  =  — 4 

"  "  log  .005  =  — 3  ' 

"  "  log  62893=     4 

3.  To  Find  the  Logarithm  of  a  Number  of  Four 
Figures  or  Less. 

If  the  number  has  less  than  four  figures  add  ciphers  on  the 
right  until  it  has  four  figures,  and  then  proceed  in  the  manner 
described  below. 

If  the  number  has  four  figures,  enter  the  table  in  the  left 
hand  column  of  the  page,  the  column  marked  N,  with  the 
first  three  figures  (the  first  three  significant  figures  if  the 
number  is  a  decimal  fraction)  and  with  the  fourth  figure  in  the 
line  running  across  the  page  at  the  extreme  top  or  bottom. 
Go  across  the  page,  in  the  line  containing  the  first  three 
figures,  until  the  column  marked  by  the  fourth  figure  is 
reached.  The  three  figures  found  at  this  point  are  the  last 
three  figures  of  the  mantissa.  The  first  two  figures  of  the 
mantissa  are  printed  only  in  the  first  column  of  the  body  of 
the  table,  and  if  they  are  not  found  in  the  same  line  with  the 
last  three  figures  they  will  be  found  a  few  lines  above. 

Suppose  the  number  is  48.65.  We  find  486  in  the  N column 
on  page  9 ;  and  the  column  marked  5  at  the  top  and  bottom  is 
the  one  to  the  right  of  the  heavy  line  down  the  middle  of  the 
page.  The  three  figures  in  this  column  and  on  the  same  line 
with  486  are  708,  which  are  the  last  three  figures  of  the 
mantissa;  the  first  two  figures  are  68.  Hence,  mantissa  of 
log  48.65  is  .68708.  By  II.  §  2  characteristic  of  log  48.65  is  1. 
Hence,  log  48.65  =  1.68708. 

Find  log  6.2.     Annexing  two  ciphers,  this  becomes  6.200. 


Xll  EXPLANATION   OF   THE   TABLES. 

Proceeding  then  as  above,  we  find  that  the  mantissa  is  79239. 
Hence,  log  6.2  =  0.79239. 

Find  log  431.  Annexing  one  cipher  this  becomes  431.0. 
Hence,  the  mantissa  is  63448;  and  log  431.  =  2.63448. 

An  important  exception  in  one  point  of  the  usual  procedure 
is  exemplified  below.  Find  log  .07416.  Entering  the  table  on 
page  14,  line  741,  we  find  in  the  column  marked  6,  the  figures 
*017.  The  asterisk  is  inserted  to  indicate  that  the  first  two 
figures  of  the  mantissa  are  to  be  taken  from  the  line  below, 
instead  of  from  above.  Hence,  the  mantissa  of  log  .07416  is 
.87017 ;  and  by  III.  §  2  log  .07416  =  2.87017.  The  negative 
sign  is  written  over  the  characteristic,  instead  of  before  it,  as 
it  applies  to  the  characteristic  only,  the  mantissa  being  positive. 

The  reason  for  placing  this  asterisk  in  the  table  is  easily 
seen.  The  last  logarithm  that  begins  with  86  is  86999.  The 
next  one  in  order  is  87005,  but  as  this  comes  in  the  middle  of 
the  page  there  is  not  room  to  print  87  in  the  same  column  with 
005,  so  the  asterisk  is  inserted  to  call  the  computer's  attention 
to  this  fact  and  bid  him  take  the  first  two  figures  from  below. 

Verify  the  following  statements  : 

log  863.2   =2.93611  log  3  =0.47712 

log  1.29      =0.11059  log  2758     =3.44059 

log  18000   =4.25527  log  64.58   =1.81010 

log  .92        =1.96379  log  .00006  =  5.77815 

log  .04312  =  2.63468  log  .00183  =  3.26245 

It  is  proper  at  this  point  to  explain  that  in  practical  com- 
putation negative  characteristics  are  very  rarely  used.  Their 
use  is  avoided  by  adding  10  to  the  characteristic  and  writing 
— 10  after  the  logarithm.  In  this  way  the  true  value  of  the 
logarithm  is  not  changed.  With  this  modification  the  four 
logarithms  above  with  negative  characteristics  become 

log  .92       =9.96379  —  10  log  .00006  =  5.77815  — 10 

log  .04312  =  8.63468  —  10  log  .00183  =  7.26245  — 10 

This  method  will  be  used  exclusively  in  the  examples  which 
follow.  After  a  little  practice  the  — lO's  written  after  the  log- 
arithm may  be  omitted  without  danger  of  error  in  the  final 


EXPLANATION   OF   THE   TABLES. 

result.  Eule  III.  §  2  can  be  changed,  therefore,  to  the  fol- 
lowing: 

The  characteristic  of  the  logarithm  of  a  number  less  than  unity 
is  formed  by  subtracting  from  9  the  number  of  ciphers  between  the 
decimal  point  and  the  first  significant  figure,  and  writing  — 10 
after  the  logarithm. 

Verify  the  following  statements : 

log  .3628  =  9.55967  —  10  log  .0026  =  7.41497  — 10 

log  .0796  =  8.90091  — 10  log  .007   =7.84510  —  10 

4.  To  Find  the  Number  to  Four  Figures  which 
Corresponds  to  a  Given  Logarithm. 

The  method  is  best  explained  by  an  example.  Given  log  x 
=  1.79683,  to  find  x.  Disregarding  the  characteristic  for  the 
moment,  we  enter  the  table  with  the  first  two  figures  of  the 
mantissa,  79,  looking  for  them  in  the  column  headed  with  0. 
We  find  them  on  page  12.  We  then  look  in  that  part  of  the 
body  of  the  table  which  contains  the  logarithms  beginning 
with  79,  for  the  number  nearest  to  683 ;  we  find  685. 

The  logarithm  in  the  table  nearest  to  our  given  logarithm  is 
now  located.  The  first  three  figures  of  the  corresponding 
number  are  taken  from  the  column  JV,  on  the  same  line  with 
685.  They  are  626.  The  fourth  figure  of  the  number  is  that 
which  stands  at  the  top  of  the  column  containing  685.  It  is 
4.  Hence,  the  number  is  6264.  To  insert  the  decimal  point 
we  note  that  the  characteristic  of  the  given  logarithm  is  1 ; 
hence,  we  must  have  two  figures  before  the  decimal  point. 
We  have,  therefore,  x  =  62.64. 

Given  log  x  =  7.14168  —  10  find  x.  The  nearest  logarithm 
in  the  table  is  .14176,  on  page  2  (notice  the  asterisk).  The 
corresponding  number  is  1386.  The  real  value  of  the  charac- 
teristic is  7  — 10  =  — 3.  Hence  by  III.  §  2  there  must  be  two 
ciphers  between  the  decimal  point  and  the  first  significant 
figure.  We  can  also  obtain  the  number  of  ciphers  by  sub- 
tracting the  augmented  characteristic  7,  from  9,  according  to 
the  rule  above.  The  result  is,  therefore,  x  =  .001386. 


XIV  .  EXPLANATION   OF   THE   TABLES. 

Verify  the  following  statements : 

log  x  =  1.73682,  x  =  54.55  log  x  =  9.74464  — 10,  x  =  .5554 

log  x  =  5.41621,  x  =  260700         log  x  =  4.48493,  x  =  30540 

log  x  =  8.91929  —  10,  x  =  .08304          log  x  =  3.14139,  x  =  1385 

log  x  =  2.43625,  x  =  273.1  log  x  =  7.79012  — 10,  x  =  .006168 

log  x  =  .64443,  x  =  4.41  log  x  =  6.56822  —  10,  x  =  .00037 

5.  Exercises  and  Examples. 

1.  Compute  the  value  of  (1.789)5. 

By  III.  §  1,  we  have  log  (1.789)6  =  5  X  log  1.789. 
log  1.789     =   .25261 

5 

log  (1.789)5  =  1.26305        .-.      (1.789)*  =  18.33 

2.  Compute  the  value  of  728  X  63.86  X  -4792 

log  728=  2.86213 
log  63.86=  1.80523 
log  .4792  =  9.68052  — 10 

by  I.  §  1,  log  (728  X  63.86  X  -4792)  =  j       14-34788  - 10 

>•  or    4.34/88. 
Hence  728  X  63.86  X  -4792  =  22280. 

3.  Compute  the  value  of  V  73. 

log  73  =  1.86332. 

By  IV.  \  1,  log  ^]T¥=  *  log  73  =  .62111, 

^'73=      4.179 

In  dividing  log  73  by  3,  the  division  is  not  exact.  Such  cases 
arise  with  great  frequency  in  logarithmic  work ;  and  the  student 
must  carefully  observe  the  two  following  rules : 

(1.)  Never  carry  the  work  beyond  the  number  of  decimal  places 
given  in  the  table,  that  is  with  this  table,  five  places. 

(2.)  When  the  division  is  not  exact,  always  take  in  the  last  place 
the  figure  that  is  nearest  to  the  true  result. 

Thus,  in  the  case  just  above,  where  we  divide  1.86332  by  3,  the 
last  step  of  the  division  is  2  divided  by  3.  Now  3  goes  into  2  more 
nearly  once  than  no  times ;  hence,  we  take  1  for  the  last  figure. 
Sometimes,  when  the  divisor  is  an  even  number,  the  result  falls 
just  half  way  between  two  integers  in  the  last  place.  We  then 
take  at  pleasure  either  the  larger  or  smaller  of  these  two  figures 
for  the  last  figure.  The  following  example  illustrates  this : 

4.  Find  1/471L  log  4711  =  3.67311, 

.-.      log  V/4711  J  log  4711  =  1.83655  or  1.83656. 

Both  of  these  logarithms  give  68.64  as  the  result  to  four  figures. 


EXPLANATION   OF   THE   TABLES.  XV 


5.  Find  y/.06398. 

log  .06398  =  8.80604  — 10. 

We  cannot  divide  this  logarithm  by  7  without  getting  an  awk- 
ward result.    But  if  we  add  and  subtract  60,  we  have 

log  .06398  =  68.80604  —  70, 

where  the  number  subtracted  from  the  logarithm  is  now  ten  times 
the  number  by  which  we  must  divide  ;  and  hence,  after  the  divi- 
sion, it  will  be  reduced  to  10.  This  is  the  best  practice  for  such 
cases.  Performing  the  division,  we  have 


log  >/.06398  =  9.82943  —  10,  .'.  1/.06398  =   .6752. 


log  l/"27"  =  £log27  =*  X  1.43136=  .71568 
log  (9.261)?  =  f  log  9.261  =  f  X  0.96666  =  .41428 
BylLgl  logz  =  .30140 

x  =  2.002. 


7.     x=        68.96X^^228  ^ 

39  X  (8.642)*  X  (.96)2 


log  68.96=   1.83860 


log  f  .4228  =  I  log  (.4228)  =  £  X  29.62613  —  30  =   9.87538  —  10 
log  of  numerator  =  11.71398  —  10 

log  39  =   1.59106 

log      (8.642)*  =  f  log  8.642  =  f  X  0.93661  =   1.56102 
log  (.96)2  =  2  log  (.96)  =  2  X  9.98227  —  10  =  19.96454  —  20 

f       23.11662-20 
log  of  denominator  =  {  QJ.    Q  U662 

log  x  =  log  of  numerator  —  log  of  denominator  =  8.59736  —  10. 
Hence  x  =  .03957. 

In  order  to  explain  clearly  each  step  in  working  this  example, 
the  amount  of  written  work  set  down  is  much  greater  than  is 
allowable  in  ordinary  practice.  The  work  for  the  same  example 
is  arranged  below  in  more  concise  form,  and  at  the  same  time  the 
— 10's  are  omitted  from  the  logarithms  with  negative  character- 
istics. 

log  39  =  1.59106  log  68.96        =  1.83860 

log  (8.642)  *        =1.56102  log  ^.4228    =9.87538 

log  (.96)2  =  9.96454  log  of  num.  =  1.71398 

log  of  denom.  =  3.11662  3.11662 

x=   .03957        log  a;  =  8.59736 


XVI  EXPLANATION   OF   THE   TABLES. 


EXAMPLES. 

Find  the  values  of  the  following  numerical  expressions,  and 
give  the  results  to  four  significant  figures : 


1.  839.6  X  /6129.  Ans.  65730  5  21  .  38  X  6.296  X.  412.   Ans.  .2292 

7  X  ^  41290 


2.  19.63X^6^2.  ^n,  173.4    4.19X6.2X^^67 

(3.339)s  X  142.9 


7    298.7  X  563  X/TT       Am.  7266 

(2.96)* 


.  ft    (9.8)3X^.4621X18. 

F  12  X  Vl7  1/41.63  X  (2.649)5 

6.  The  Arithmetical  Complement  of  the  Logarithm 

or    Co-logarithm.      To  compute    the  value    of  -  by  log- 

b 

arithms,  we  may  take  either  log  a  —  log  b,  or  log  a  -f-  log-. 

b 

Log  -  =  log  1  —  log  b  =  0  —  log  b  is  called  the  co-logarithm  of 
b 

b.     We  have,  therefore,  the  following  rule : 

To  form  the  co-logarithm  of  a  given  number  subtract  the  log- 
arithm of  the  number  from  0. 

It  is  customary  in  practice  to  subtract  the  logarithm  from 
10  instead  of  from  0,  and  then  to  write  — 10  after  the  result ; 
that  is,  the  logarithm  is  subtracted  from  0,  written  in  the  form 
10.00000 — 10.  If  the  logarithm  is  one  which  has  been  itself 
augmented  by  10,  the  two  — 10's,  that  in  the  subtrahend  and 
that  in  the  minuend,  cancel  each  other. 

Ex.  Find  colog  729.6.  Log  728.6  =  2.86308.  Subtracting  this 
from  10.00000  — 10,  the  result  is  colog  729.6  =  7.13692  — 10. 

Ex.  Find  colog  .0641.  Log  .0641  =  8.80686  —  10.  Subtracting 
this  from  10.00000—  10,  the  result  is  colog  .0641  =  1.19314. 

Verify  the  following  statements : 

colog  9986  =  6.00061,  colog     3.9  =  9.40894, 

colog  7.298  =  9.130SI ),  colog  380.6  =  7.41953, 

colog  .4682  =   .32957,  colog  .005    ==  2.30103. 


EXPLANATION   OF   THE   TABLES.  XV11 

With  a  little  practice  the  student  can  write  down  the  colog 
directly  from  the  table,  as  readily  as  the  log  itself.  The  prac- 
tical rule  is  to  subtract  each  figure  of  the  logarithm,  beginning 
at  the  left,  from  9,  except  the  last  or  right-hand  figure,  which 
must  be  subtracted  from  10.  When  the  characteristic  of  the 
logarithm  is  0,  care  must  be  taken  not  to  forget  to  subtract 
this  from  9,  just  as  any  other  characteristic  would  be  sub- 
tracted. 

The  practical  advantage  of  using  cologs  consists  in  the  fact 
that  thereby  the  number  of  separate  operations  required  to 
obtain  the  log  of  the  result  is  reduced.  For  example,  suppose 

we  wish  to  calculate  log  —^ — ^-^.    Without  using  co  =  logs 
three  operations  are  required : 

(1.)  to  find  log  a  +  log  6  -4-  log  c, 
(2.)  «  logd  +  loge  +  log/, 
(3.)  to  subtract  (2)  from  (1). 

If,  on  the  other  hand,  cologs  are  used,  these  three  opera- 
tions are  reduced  to  one,  viz. :  to  find  log  a  -4-  log  b  -\-  log  c  -f- 
colog  d  -f-  colog  e  -f  colog  /. 

Ex.  By  using  cologs  the  work  of  Ex.  7,  p.  xv.,  may  be  arranged 
in  the  following  concise  form : 

log  68.96  =  1.83860 
log  1^.4228  =  9.87538 
colog  39  =8.40894 
colog  (8.642)1  =8.43898 
colog  (.96)2  ==  0.03546 
logo;  =8.59736 

7.  To  Find  the  Logarithm  of  a  Number  which 
Consists  of  Five  Figures. 

This  is  accomplished  by  the  aid  of  the  operation  known  as 
interpolation.  Let  the  given  number  be  31.687.  The  table 
gives  log  31.68  =  1.50079  and  log  31.69  =  1.50092.  To  find 
log  31,687  a  small  correction  must  either  be  added  to  log  31.68 
or  subtracted  from  log  31.69. 

The  whole  difference  between  two  consecutive  logarithms  in 


XV111  EXPLANATION   OF   THE   TABLES. 

the  table  is  called  the  tabular  difference.  In  this  case  the 
tabular  difference  is  13.  That  is,  the  logarithm  increases  by 
13  for  a  change  of  unity  in  the  fourth  place  in  the  number. 
Hence,  for  7  in  the  fifth  place  the  proportional  change  in  the 
logarithm  will  be  seven-tenths  of  13,  or  9.1,  the  nearest  integer 
to  which  is  9 ;  hence,  9  is  the  correction  to  be  added  to  log 
31.68  to  obtain  31.687.  Therefore, 

log  31.687  =  1.50079  +  .00009  =  1.50088 

This  method  of  determining  the  correction  for  the  fifth 
figure  is  not  theoretically  correct,  for  it  assumes  that  log- 
arithms vary  proportionally  with  the  corresponding  numbers; 
but  while  this  is  not  true,  it  is  applied  here  for  such  a  small 
interval  that  no  appreciable  error  arises  from  its  use. 

The  work  of  computing  corrections  for  the  fifth  figure  is 
performed  in  the  little  auxiliary  tables  in  the  column  headed 
Prop.  Pts.  (Proportional  Parts).  On  the  same  page  with  log 
31.68  we  find  one  of  these  tables  headed  by  the  tabular  differ- 
ence 13.  In  this  table  we  look  in  the  column  to  the  left  of 
the  vertical  line  for  the  fifth  figure,  7,  of  the  given  number. 
The  corresponding  number  to  the  right  of  the  vertical  line, 
which  is  9.1,  is  the  required  correction,  the  nearest  integer  to 
which  must  be  added  to  the  logarithm  corresponding  to  the 
first  four  figures  of  the  given  number. 

The  student  should  accustom  himself  to  apply  the  correc- 
tion for  the  fifth  figure  mentally,  and  to  write  nothing  on  the 
paper  except  the  corrected  logarithm. 

Verify  the  following  statements  : 

log  414.23  =  2.61724,  log  69.426  =  1.84152, 

log  3.8642  =  0.58706,  log  1418.1  =  3.15171 , 

log  .43007  =  9.63354,  log  85672.  =  4.93284. 

8.  To  Find  the  Number  to  Five  Figures  Corres- 
ponding to  any  Logarithm. 

Let  logo;  =  2.38647.  Look  in  the  table  for  the  nearest  man- 
tissa that  is  less  than  38647,  not  for  that  which  is  absolutely 


EXPLANATION   OF   THE   TABLES.  XIX 

nearest,  as  when  only  four  figures  are  required.  This  is  found 
to  be  38632,  which  corresponds  to  the  natural  number  2434. 
These  are  the  first  four  figures  of  x.  Next  find  the  tabular 
difference,  which  is  18.  Then  subtract  the  mantissa  taken 
from  the  table  (38632)  from  the  mantissa  of  the  given  log- 
arithm (38647);  the  difference  is  15.  Hence,  we  have  the 
problem:  If  a  difference  of  18  in  the  mantissse  makes  a 
change  of  a  unit  in  the  fourth  figure  of  the  number,  what 
change  will  be  made  by  a  difference  of  15  in  the  mantissse  ? 
Evidently  we  have  the  proportion 

18 :  1  =  15  :  difference  required 
or  difference  =  i-f  =  |  =  .8  ; 

that  is,  the  correction  is  .8  of  a  unit  in  the  fourth  place,  or  8 
units  in  the  fifth  place.  Hence,  the  figures  in  the  number  x 
are  24348,  and  inserting  the  point  after  the  3,  because  the 
characteristic  is  2,  we  have  x  =  243.48. 

The  work  of  determining  the  fifth  figure  is  performed  in 
the  marginal  tables  of  Prop.  Pts.  Find  the  one  correspond- 
ing to  the  tabular  difference  IS^and  look  on  the  right  of  the 
vertical  column  for  the  number  nearest  to  15,  the  difference 
between  the  given  log  and  the  next  smaller  one  in  the  table. 
We  find  14.4  and  the  corresponding  number  on  the  left  of  the 
vertical  line,  which  is  8,  is  the  required  fifth  figure. 

Verify  the  following  statements : 

log  x  =  3.28642,  x  =  1933.8        log  x  =  7.63419  — 10,  x  =  .0043072 

log  x  =  1.46010,  x  =  28.847        log  x  =  2.31419,  x  =  206.15 

log  x  =  9.38642  — 10,  x  =  .24346        log  x  =   .76787,  x  =  5.8596 

9.  Exercises  and  Examples. 

_  (36.842)*  X. (1.6272)' X  &_   - 
~  1/.062416  X  72.983  X  ^189* 

log  (36.842)4       =  1.56634  X*=   -52211 
log  (1.6272)2       =   .21144  X  2  =   .42288 

log  87    =1.93952 

colog  V  .062416  =  1.20471  -s-  2  =   .60235 

colog  72.983  —  8.13678 

colog  ^189         =  7.72354  -=-  3  =  9.24118 

x  =  7.3252          log*=   .86482 


XX  EXPLANATION  OF  THE  TABLES. 


EXAMPLES. 

In  working  these  examples  use  cologs  wherever  necessary,  and 
arrange  the  work  as  on  preceding  page. 

67.284  X  .10003 
L       f  74^99X6.7843'  ^..10953 


63.842  X 
(42.32)*  X(.02478)3- 1/2 

(7.2S43)8  X  1^.00067894 
3"       (620.01)*  X  489.62  ^m.  306.49 


1986.1  X  ff  92.836 

3.403.75 


5. 


a 


V  1000000 
7.     1/IO~X  ^100  X  HOW!  ^m.  82.542 


10.  Numbers  with  Six  Figures.  As  a  general  rule,  we 
cannot  work  to  six  figures  in  natural  numbers  with  a  table  of 
five-place  logarithms,  for  when  the  correction  for  the  sixth 
figure  is  applied  it  will  usually  be  too  small  to  make  any 
difference  in  the  logarithm.  On  the  first  page  or  two  of  the 
table,  however,  where  the  logarithms  vary  rapidly,  it  can  be 
done  with  approximate  accuracy. 

The  correction  for  the  sixth  figure  is  always  one-tenth  of  the 
correction  for  the  same  figure  in  the  fifth  place. 

Ex.    To  find  log  13.9647. 

log  13.96  =  1.14489 
correction  for  fifth  figure  =  12.4 

"  "   sixth    "      =   2.17 

total  correction  =  14.57,  nearest  integer  =  _  15 

log  13  9647   =1.14504 


EXPLANATION  OF  THE  TABLES.          XXi 

Ex.    Find  a,  given  log  x  —  2.21647, 

nearest  log  in  table  =  .21643,  corresponding  to  1646 

difference  4 

nearest  smaller  prop.1 

pt.  under  tab.  diff.  26  /  = ^  J  corresponding  to  1 

difference  remaining  ~IA  *  for  the  fafth  ^ 

1.4  X 10  (because  sixth  figure  is  required)  =  14,  corresponding  to 
5  for  the  sixth  figure.     Hence,  x  =  164.615. 

Verify  the  following: 

log  1219.35  =  3.08613.  log  x  =  3.12964,     x  =  1347.84. 

log  10.7642  =  1.03198.  log  x  =  0.06432,     x  =  1.15963. 


TABLE  II.     Constants  and  Their  Logarithms.     (Page  #0.) 

11.  No  description  of  this  table  is  necessary.  The  loga- 
rithms are  given  to  seven  places,  instead  of  five,  in  case  a 
greater  degree  of  accuracy  should  be  required.  If  only  the  first 
five  places  are  used,  the  fifth  figure  must  be  increased  by  1,  if 
the  sixth  figure  is  5,  or  more. 


TABLE  III.     Logarithmic  Sines,  Cosines,  Tangents  and 
Cotangents.     (Pages  21-66.) 

12.  The  logarithms  of  the  trigonometric  functions  are  used 
in  computation  much  more  frequently  than  the  functions  them- 
selves, which  are  called  natural  functions.  For  this  reason  this 
table  is  given  more  prominence  than  that  of  the  natural  func- 
tions. The  table  gives  the  logarithms  of  the  functions  for  each 
minute  from  0°  to  90°.  The  functions  of  angles  not  expressed 
evenly  in  minutes  can  be  found  by  interpolation,  as  explained 
below. 

Since  sec  and  esc  are  the  reciprocals  of  cos  and  sin  respec- 
tively, their  logs  can  always  be  found  by  taking  the  cologs  of 
the  latter. 

The  sin  and  cos  of  all  angles  and  the  tan  of  angles  less  than 
45°  are  less  than  unity ;  hence,  their  logarithms  have  negative 
characteristics.  For  this  reason  the  characteristics  of  all  these 
logarithms  are  increased  by  10  in  the  tables. 


XXU          EXPLANATION  OF  THE  TABLES. 

13.  To  Find  the  Logarithmic  Function  of  an  Angle 
Less  than  90°. 

Enter  the  table  with  the  given  number  of  degrees,  which 
will  be  found  at  the  top  of  the  page,  if  it  is  44°  or  less,  but  at 
the  bottom  of  the  page,  if  it  is  greater  than  44°.  The  func- 
tion required  is  read  at  the  top  or  bottom  of  the  page,  accord- 
ing as  the  number  of  degrees  is  at  the  top  or  bottom,  and  the 
required  logarithm  is  taken  from  the  corresponding  column. 
The  minutes  are  read  in  the  left  hand  column  of  the  page,  if 
the  degrees  are  read  at  the  top,  but  in  the  extreme  right  hand 
column  of  the  body  of  the  table  if  the  degrees  are  read  at  the 
bottom. 

EXERCISES. 

1.  Find  log  sin  24°  38'.    24°  is  at  the  top  of  page  46,  and  the  log 
sin  column  for  24°  is  the  first  column  of  logarithms  on  the  page. 
Running  dow.n  the  page  until  we  corne  to  38',  we  find  log-sin  24° 
38' =  9.61994. 

2.  Find  log  tan  57°  16'.    57°  is  at  the  bottom  of  page  54.     Run- 
ning up  the  page  in  the  column  marked  at  the  bottom  log  tan, 
until  we  come  to  the  line  with  16'  on  the  right,  we  find  log  tan 
57°  IV  =  0.19192. 

Verify  the  following  statements: 

log  sin  39°  16'  =  9.80136,  log  cos    8°  19'  =  9.99541, 

log  tan  63°  24'  =  0.30037,  log  cot  54°    9'  =  9.85887, 

log  cos  41°  31'  =  9.87434,  log  tan  82°  56'  =  0.90670, 

log  cot  26°  12'  =  0.30798,  log  cot    7°         =  0.91086, 

log  cos  31°        =  9.93307,  log  sin  19°  12'  =  9.51702. 

14.  Interpolating  for  Seconds. 

Find  the  logarithmic  functions  for  the  degrees  and  minutes  as 
before;  then  apply  a  correction  for  the  seconds,  as  explained  below. 
This  correction  must  be  added  if  the  function  is  sin  or  tan,  and 
subtracted  if  the  function  is  cos  or  cot. 

Find  log  sin  16°  28'  35". 

log  sin  16°  28'  =  9.45249,  and  the  tabular  difference  is  43 ;  that 
is,  the  log  sin  increases  by  43,  while  the  angle  increases  by  1'. 
Hence,  the  proportional  increase  for  1"  is  f  $ ,  and  for  35"  it  is 
U  X  35  =  JVVL  =  25.08  . . . ,  the  nearest  integer  to  which  is  the 
required  correction.  Hence, 

log  sin  16°  28'  35"  =  9.45249  +  .00025  =  9.45274. 


EXPLANATION    OF   THE    TABLES.  XX111 

The  auxiliary  table  of  proportional  parts  for  tabular  differ- 
ence 43  will  give  the  same  result.  The  column  to  the  left  of 
the  vertical  line  in  these  auxiliary  tables  gives  the  number  of 
seconds,  arranged  in  the  order  6,  7,  8,  9,  10,  20,  30,  40,  50. 
If  the  correction  for  1,  2>  3,  4,  or  5  seconds  is  required  it  is 
obtained  by  taking  one-tenth  of  that  for  10,  20,  30,  40,  or  50 
respectively.  The  work  can  be  arranged  concisely  as  follows, 
but  it  is  desirable  in  actual  practice  to  compute  the  correction 
mentally  and  to  write  only  the  complete  logarithm : 

log  sin  16°  28'  =  9.45249 
correction  for  30"  =         21.5 
"  "     5"  =  3.58 

log  sin  16°  28'  35"  =  9.45274 

Find  log  cot  61°  13'  19".  log  cot  61°  13'  =  9.73987 

correction  for  10"  (tab.  diff.  30)     =  5.0 

u  u     g//          «         «        __   45 

nearest  integer  to  total  correction  =  10.0 

Subtract  correction  because  function  is  cot,  10 

log  cot  61°  13'  19"  =  9.73977 

On  pages  22  to  27  of  the  table,  on  account  of  the  large 
number  of  differences  which  occur,  owing  to  the  rapid  varia- 
tion of  the  logarithms,  different  arrangements  of  the  tables 
of  Prop.  Pts.  are  made.  If  the  logarithm  required  falls  on 
pages  25  to  27,  and  it  happens  that  the  tabular  difference  is 
one  for  which  a  table  of  proportional  parts  is  given,  the  pro- 
cedure is  the  same  as  above;  otherwise  as  follows: 

Find  log  tan  3°  51'  26" 

log  tan  3°  51'  =  8.82799,  tab.  diff.  =  188. 

This  tabular  difference  is  not  given,  so  we  use  the  auxiliary 
tables  for  185  and  3  (because  185  -f  3  =  188)  instead. 

tab.  diff.  185  (  Correction  for  20"  =  61.7 
"     6"  =  18.5 

tab.  diff.    3   {  '   »?"   1-0 

I  "          "     6"=   0.3 


81.5 
Hence,  the  total  correction  to  be  added  is  82  and  log  tan  3° 

61'  26"  =  8.82881. 


XXIV  EXPLANATION   OF   THE   TABLES. 

In  a  case  of  this  kind  it  is,  perhaps,  just  as  easy  to  compute 
the  correction  without  using  the  auxiliary  tables. 

On  pages  22  to  24  the  Prop.  Pt.  is  given  for  one  second  for 
each  tabular  difference  for  log  sin,  log  tan,  and  log  cot.     Log 
cos  varies  so  slowly  in  this  part  of  the  table  that  no  auxiliary 
tables  are  necessary. 
Find  log  sin  1°  48'  53". 

log  sin  1°  48'  =  8.49708,  tab.  diff.  =  400 
Prop.  pt.  for    1"  (tab.  diff.  400)  =     6.67 
"        "    53"  =  6.67X53        =353.51 
.  \    correction  to  be  added          =  354. 
and  log  sin  1°  48'  53"  =  8.49708  +  .00354  =  8.50062 
On  account  of  the  very  rapid  variation  in  the  log  sin  and 
log  tan  at  the  beginning  of  the  table,  the  theory  that  the  varia- 
tion of  the  log  is  proportional  to  that  of  the  angle,  leads  to 
results  which  are  sometimes  appreciably  in  error.     For  this 
reason,  when  great  precision  is  required,  Table  IV.,  pp.  67,  68, 
should  be  used  in  finding  the  log  sin  and  log  tan  of  angles  less 
than  4°.     An  explanation  of  this  table  is  given  below,  §  19. 
Yerify  the  following  statements  : 

log  cos  17°  38'  42"  =  9. 97907,  log  tan    5°  38'    5"  =  8.99416, 

log  tan  84°    9'  13"  =  0.98972,       ^log  sin     1°  12'  38"  =  8.32482, 
log  sin  61°  41'  31"  =  9.94469,  log  cos  26°  28'  37"  =  9.95188, 

log  cos  87°    6'  14"  =  8.70351,  log  cot    9°    1'  43"  =  0.79889, 

log  cot  86°  53'  34"  =  8.73467,  log  sin  45°  43'  28"  =  9.85491. 

15.  To  Find  the  Logarithmic  Function  of  an  Angle 
>90°. 

According  to  the  theorems  demonstrated  in  Elements  of 
Trigonometry  §§  28-31,  and  the  rules  on  page  40,  summariz- 
ing the  results,  the  functions  of  any  angle  can  be  found  if 
those  of  all  angles  less  than  90°  are  known.  These  results 
are  given  here  in  the  form  of  the  following  rules: 

I.  To  find  the  function  of  an  angle  between  90°  and  180°  sub- 
tract the  angle  from  180°  and  look  for  the  same  function  of  the 
difference,  or  subtract  90°  from  the  angle  and  look  for  the  co-function 
of  the  difference. 

II.  To  find  a  function  of  an  angle  between  180°  and  270°  sub- 
tract the  angle  from  270°  and  look  for  the  co-function  of  the  differ- 


EXPLANATION  OF  THE  TABLES.          XXV 

ence,  or  subtract  180°  from  the  angle  and  look  for  the  same  function 
of  the  difference. 

III.  To  find  a  function  of  an  angle  between  270°  and  360°  sub- 
tract the  angle  from  360°  and  look  for  the  same  function  of  the  differ- 
ence, or  subtract  270°  from  the  angle  and  look  for  the  co-function 
of  the  difference. 

The  second  alternative  in  each  of  these  rules  is  better  if  the 
angle  has  minutes  and  seconds,  for  there  is  less  danger  of 
making  a  mistake  in  taking  the  difference. 

EXERCISES. 

1.  Find  log  cos  117°  19'  35". 

By  rule  I.  log  cos  117°  19'  35"  =  log  (—sin  27°  19'  35"). 

NOTE.— In  taking  the  logarithm  of  a  negative  quantity  we  pro- 
ceed as  if  the  quantity  were  positive.  To  the  logarithm  when 
found,  we  prefix  the  symbol  (— )  or  annex  the  symbol  n.  Neither 
of  these  signs  affect  the  operations  to  which  the  logarithm  may  be 
subjected,  but  are  used  merely  to  remind  the  computer  that  the 
corresponding  numbers  are  negative. 

log  sin    27°  19'  35"  =         9.66187, 
log  cos  117°  19'  35"  =  (— )  9.66187. 

2.  Find  log  tan  242°  20'  17". 

By  rule  II.  log  tan  242°  20'  17"  =  log  tan  62°  20'  17"  =  0.28054. 

Verify  the  following  statements  : 

log  sin  300°  24'  =  (— )  9.93577  log  cot  200°  30'  30"  =  0.42707 
log  cos  216°  14'  33"  =  (— )  9.90662  log  sin  138°  48'  6"  =  9.81867 
log  tan  101°  6'  52"  =  (— )  0.70674  log  cos  342°  38'  15"  =  9.97975 

16.  To  Find  an  Angle  Given  one  of  its  Logarith- 
mic Functions. 

A  further  glance  at  the  general  constitution  of  the  table  is 
first  necessary.  Upon  each  page  of  the  table  are  four  columns 
of  logarithms,  the  first  and  fourth  are  logarithmic  sines  and 
cosines,  the  second  and  third  are  logarithmic  tangents  and 
cotangents.  The  logarithms  increase,  going  toward  the  back 
of  the  table  in  the  first  and  second  columns,  and  then  passing 
into  the  fourth  and  third  columns  respectively,  they  increase, 
going  toward  the  front  of  the  table.  Eemembering  this,  the 
place  of  any  given  logarithm  in  the  table  can  be  found  readily. 


XXVI  EXPLANATION   OF   THE   TABLES. 

The  rules  for  finding  an  angle  from  its  logarithmic  function 
are  as  follows: 

If  the  given  function  is  log  sin  or  log  cos  look  for  the  nearest 
smaller  logarithm  in  the  first  or  fourth  column ;  if  it  is  log  tan  or 
log  cot,  look  in  the  second  or  third  column. 

Read  the  degrees  at  the  top  or  bottom  of  the  page,  according  as 
the  name  of  the  given  function  is  at  the  top  or  bottom  of  the  column 
in  which  the  given  logarithm  is  located. 

Head  the  minutes  on  the  left  or  right  according  as  the  degrees 
are  read  at  the  top  or  bottom  of  the  page,  and  in  the  same  line 
with  the  nearest  logarithm  smaller  than  the  given  one. 

Determine  the  number  of  seconds  by  proportion  and  add  them  to 
the  degrees  and  minutes  found,  if  the  given  function  is  log  sin  or 
log  tan,  but  subtract  them  if  it  is  log  cos  or  log  cot. 

EXERCISES. 

1.  Given  log  sin  6  =  9.86592,  what  is  6? 

In  the  fourth  column  on  p.  64  we  find  9.86589,  and  log  sin  is 
read  at  the  bottom.  Hence,  the  degrees  and  minutes  are  47°  15'. 
The  tabular  difference  is  11  and  the  difference  between  the  given 
log  and  log  sin  47°  15'  is  3.  Hence,  0  exceeds  47°  15'  by  T3T  of  one 
minute.  This  fraction  reduced  to  seconds  is  T3T  X  60  — 16".  Hence, 
0  =  47°  15' 16". 

To  use  the  auxiliary  table  to  find  the  number  of  seconds,  we 
arrange  the  work  as  follows,  using  table  for  tabular  difference  11. 
whole  difference  =  3 

nearest  smaller  prop.  pt.  =  1.8,  corresponding  to  10" 
difference  remaining        =  1.2  "  "     6" 

whole  number  of  seconds  16" 

NOTE. — The  number  of  seconds  corresponding  to  1.2  under  tabular 
difference  11  is,  according  to  the  table,  either  6"  or  1"  ;  but  6"  is 
really  a  little  nearer  than  7",  as  we  found  above. 

2.  Given  log  cot  0  =  0.72654,  find  0. 

On  p.  32,  in  the  third  column,  we  find  0.72643,  and  log  cot  is 

read  at  the  top  ;  hence,  the  degrees  and  minutes  are  10°  38'.    The 

tabular  difference  is  70,  and  the  difference  between  log  cot  6  and 

0.72643  is  11.    Hence,  using  table  of  proportional  parts,  we  have 

whole  difference  =11 

nearest  smaller  prop.  pt.  =  10.5,  corresponding  to  9" 
difference  remaining    =     .6, 


EXPLANATION   OF   THE   TABLES.  XXV11 

as  this  is  less  than  half  the  prop.  pt.  for  1"  (1.17),  the  entire  correc- 
tion is  9",  which  is  subtracted  from  10°  38',  giving  0  =  10°  37'  51". 

3.  Given  log  tan  6  =  8.61246,  find  6. 
On  page  24,  log  tan  2°  20'  =  8.61009. 

difference          =  237,  tab.  diff.  =  310,  prop.  pt.  for  1"  =  5.17, 

no.  of  seconds  =  ^-  =  46".        .-.0  =  2°  20'  46". 
5.17 

In  these  three  exercises  the  results  are  incomplete,  because  we 
know  from  Trigonometry  that  there  are  always  two  angles  less 
than  360°  corresponding  to  any  given  trigonometric  function. 
The  complete  answers  are  as  follows :  1.  6  =  47°  15'  16"  and  180°— 
47°  15'  16"  =  132°  44'  44",  because  sin  6  is  positive  in  the  first  and 
second  quadrants.  2.  6  =  10°  37'  51"  and  180°  -f  10°  37'  51"  =  190° 
37'  51".  3.  6  =  2°  20'  46"  and  180°  +  2°  20'  46"  =  182°  20'  46",  be- 
cause tan  0  and  cot  6  are  positive  in  the  first  and  third  quadrants. 

4.  Given  log  cos  6  =  (— )  9.62983,  find  0. 

Assume  that  cos  6  is  positive  and  find  the  angle  corresponding 
to  it  in  the  first  quadrant.    We  find  on  p.  47  log  cos  64°  46'  =  9.62972. 
whole  difference  =  11 

nearest  smaller  prop.  pt.  =  9.0,  corresponding  to  20" 
difference  remaining      =   2.0  "  "     4" 

number  of  seconds  to  be  subtracted,  24" 

Hence,  log  cos  64°  45'  36"  =  9.62983. 
Since  the  cos  is  negative  in  the  second  and  third  quadrants, 

we  have  d  -  /  180°  ~  64°  45/  36//  =  115°  14/  24// 

\  180°  +  64°  45'  36"  =  244°  45'  36". 

When  one  or  both  values  of  the  required  angle  are  not  in  the 
first  quadrant,  the  following  rules  are  to  be  followed : 

To  find  an  angle  in  the  second  quadrant,  subtract  the  angle  taken 
from  the  table  from  180°. 

To  find  an  angle  in  the  third  quadrant,  add  the  angle  taken  from, 
the  table  to  180°. 

To  find  an  angle  in  the  fourth  quadrant,  subtract  the  angle  taken 
from  the  table  from  360°. 

Verify  the  following  statements  : 

log  sin  0=  9.28642,  0=  11°  9'  1"  and  168°  50' 59". 
log  cos  0=  8.46321,  0=  88°  20'  6"  "  271°  39'  54". 
log  tan  0=  0.12983,  0=  53°  26' 22"  "  233°  26' 22". 
log  cot  0=  9.62412,  0  ±=  67°  10' 36"  "  247°  10' 36". 
log  sin  0  =  (— )  9.96419,  0  =  247°  3'  0"  "  292°  57'  0". 
log  cos  0  =  (— )  9.78416,  0  =  127°  28'  15"  "  232°  31'  45". 
log  tan  0=(— )  9.42317,  0  =  165°  9' 36"  "  345°  9' 36". 
log  cot  0  =  (— )  8.76432,  0  =  93°  19'  35"  "  273°  19'  35". 


XXV111  EXPLANATION   OF   THE   TABLES. 

17.  Functions  of  Negative  Angles.    To  find  the  log- 
arithmic  functions   of  negative   angles,  follow  the   formulae 
given  in  §  31,  Elements  of  Trigonometry. 

18.  General  Remarks.     In  using  a  five-place  table  of 
logarithmic  functions  the  computer  should  remember  that  the 
seconds  in  his  results  will  be,  in  general,  only  approximately 
correct.     Nevertheless,  angles  can  be  determined  in  most  parts 
of  the  table  more  closely  than  to  tenths  of  a  minute ;  so  that 
it  seems  preferable  to  give  tables  of  proportional  parts  for 
seconds,  rather  than  for  tenths  of  a  minute. 

Attention  is  here  called  to  the  fact  that  throughout  all  the 
tables  a  final  five  is  sometimes  marked  with  a  small  dash  over 
it,  thus  5,  and  sometimes  it  is  not  so  marked.  This  mark  is 
used  to  indicate  that  if,  for  any  reason,  the  computer  wishes 
to  use  a  smaller  number  of  decimal  places  than  are  gwen  in 
the  table,  the  5  is  to  be  dropped  without  increasing  the  pre- 
ceding figure  by  unity.  If  the  5  is  not  marked  in  this  way 
the  preceding  figure  must  be  increased  by  unity  if  the  5  is 
dropped. 

The  student  may  vary  somewhat  the  procedure  in  the  matter 
of  interpolation  as  he  becomes  accustomed  to  using  the  tables. 
For  example :  in  finding  log  18769  he  may  take  log  1877  from 
the  tables  and  subtract  the  correction  for  1,  instead  of  taking 
log  1876  and  adding  the  correction  for  9.  Again,  in  finding 
log  cos  78°  38'  56"  he  may  take  log  cos  78°  39'  and  add  the 
correction  for  4"  instead  of  taking  log  cos  78°  38'  and  sub- 
tracting the  correction  for  56".  Numerous  points  of  this  kind, 
which  in  many  cases  will  shorten  the  work,  will  'suggest  them- 
selves, and  need  not  be  specified  here. 

EXAMPLES. 
Find  0  in  each  of  the  following  examples : 

1        n  0  -  6-2984  8ip'  63°  18/  W  6  =  / 127°  l/  7" 

"  7.5692  cot  116°  36'  12"  "  1 307°  1'  1" 

o  2.93  tan  48°  6'  38"  0=/121°34'    3" 

"  14.12  sin  26°  13'  42"  "  i  238°  25'  57" 


EXPLANATION   OF   THE   TABLES.  XXIX 

7°  58'  VI" 
172°    1'  43" 


I  sin3  146°  12'  19"  X  tan  78°  12'  32"  a  _ 
8-   8m  °  :=  \     cot*  12°  14'  6"  X  cos  64°  4'  55"  ' 

352°  V  43" 

.     a  _  .93862  cos2  312°  38'  40"          e=  f  32°  55'  19" 
4.  cot  a  :  _  - 


TABLE  IY.     (Pages  67  and  68.) 

19.  Sine  and  Tangent  of  Small  Angles.  This  table 
derives  its  usefulness  from  the  fact  that  when  an  angle  (a)  is 

small  the  ratios  ?!5L?  and  ^-^  vary  but  slowly.     The  quan- 

a  a 

tities  S  and  T  in  the  table  are  the  logarithms  (increased  by 
10)  of  these  ratios,  where  the  angle  is  expressed  in  seconds. 
Hence,  to  find  log  sin  and  log  tan  of  a  small  angle  we  have 
the  formulae 

log  sin  a  =  log  a"  +  S 

log  tan  a  =  log  a"  +  T 
and  to  find  a  small  angle  from  its  log  sin  or  log  tan  we  have 

log  a"  =  log  sin  a  —  S 

log  a"  •=.  log  tan  a  —  T 

Ex.     Find  log  tan  0°  26'  51". 

0°  26'  51"  =  1611"        log  1611  =  3.20710 

T  (for  0°  270=4.68558 

.-.     log  tan  0°  26'  51"  =  7.89268 

(the  same  calculated  from  Table  III.  is  7.89264,  which  is  thus 
shewn  to  be  in  error  four  units  in  the  fifth  place). 
Ex.     Given  log  sin  a  =  8.36892,  find  a. 
From  Table  III.  we  find  that  a  =  1°  207  approximately ; 
hence,  the  proper  value  of  S  (from  Table  IY)  is  4.68554.     We 
have,  therefore,         log  sin  a  _  s=  3>68338  =  log  a// 

a  =  4824"  -=1°  20/24". 
Yerify  the  following  statements,  by  means  of  Table  IY : 

log  sin  0°  57'  36"  =  8.22412. 

log  tan  a  =  8.19632,  a  =  0°  54'  1". 

To  find  the  cosine  or  cotagent  of  an  angle  nearly  90°  use 
the  same  table,  taking  the  sine  or  tangent,  as  the  case  may  be, 
of  the  complement  of  the  given  angle. 


XXX          EXPLANATION  OF  THE  TABLES. 

TABLE  V.    Natural  Functions.     (Pages  69-78.) 

20.  By  the  terms  natural  sine,  cosine,  etc.,  are  meant  the 
actual  values  of  these  functions.  The  table  is  used  compara- 
tively seldom,  and  for  that  reason  the  functions  are  given  for 
every  five  minutes  only.  To  find  the  functions  for  inter- 
mediate minutes  the  process  of  interpolation  by  simple  pro- 
portion is  used.  Thus,  to  find  sin  51°  18',  we  have 

sin  51°  20'  =  .78079 

sin  51°  15'  =  .77988 
difference  for  5'  =        91 
hence,  correction  for  3'  =  f  of  91   =  55, 
and  sin  51°  18'  =  .77988  +  .00055     =  .78043. 

The  rules  given  above,  for  adding  and  subtracting  correc- 
tions and  for  finding  functions  of  angles  greater  than  90°, 
apply  here  the  same  as  in  the  case  of  Table  III. 

The  results  of  interpolating  minutes  in  that  part  of  the 
table  which  gives  the  cot  of  angles  less  than  15°  and  the  tan- 
gents of  angles  between  75°  and  90°  will,  in  general,  not  be 
correct  in  the  last  place.  Hence,  when  considerable  .precision 
is  required  in  these  cases  the  function  should  be  found  by 
taking  the  natural  number  corresponding  to  the  logarithm 
found  in  Table  III. 


TABLE  VI.    Circular  Arcs  Expressed  in  Radians.    (Page  74.) 
This  table  gives  to  seven  decimal  places  the  number  of 
radians  for  every  degree  up  to  180°,  with  auxiliary  tables  for 
minutes  and  seconds. 

EXERCISES. 
L  How  many  radians  in  126°  38' 19"  ?    From  the  table  we  have 

number  of  radians  in  126°  =2.1991149 

38'  =   .0110538 

"  "  19"=  .0000921 

"  "          126°  38'  19"  =  2.2102608 

2.  How  many  degrees,  minutes  and  seconds  in  4.6832964  radians  ? 
As  this  number  of  radians  exceeds  180,  we  subtract  the  number  of 


EXPLANATION  OF  THE  TABLES.          XXXI 

radians  in  180°  and  find  the  degrees,  minutes  and  seconds  in  the 
remainder.    This  last  added  to  180°  is  the  result : 

Given  number  of  radians     =  4.6832964 
Radians  in       180°  =3.1415927 

Difference  =1.5417037 

Radians  in         88°  =  1.5358897 

.0058140 

Radians  in  19'  =   .0055269 

.0002871 

Radians  in  59"     =         2860 

Result         =         268°  19'  59"  .0000011 

The  last  difference,  .0000011,  corresponds  to  less  than  half  a 
second. 


TABLE   VII.      Napierian    Logarithms    of   Numbers.      (Pages 

75,  76.) 

Although  these  logarithms  are  not  used  for  purposes  of 
practical  computation,  their  values  are  sometimes  required  in 
calculating  values  of  transcendental  functions,  and  for  other 
purposes.  -The  table  gives  the  logarithm  of  each  number  from 
1  to  1000.  As  the  value  of  the  characteristic  does  not  depend 
upon  the  position  of  the  decimal  point,  nor  the  value  of  the 
mantissa  solely  upon  the  sequence  of  figures  in  the  corres- 
ponding number,  we  cannot  use  the  table  just  as  we  do  a 
table  of  common  logarithms.  If  log  363.8  is  required  we  can 
find  it  by  interpolating  between  log  363  and  log  364 ;  but  if 
log  3638  is  required  we  must  find  log  363.8  in  the  manner  just 
indicated,  and  then  add  log  10.  The  work  is  as  follows : 

log  363       =5.89440 

log  364       =  5.89715 

difference  =        275 

.8  of  difference  =        220 

adding  this  to  log  363  gives  log  363.8  =  5.89660 

log  10      =  2.30259 
log  3638  =  8.19919 

To  find  the  number  corresponding  to  a  given  Napierian 
logarithm  we  first  subtract  as  many  times  log  10  as  may  be 
necessary  to  bring  the  logarithm  within  the  limits  of  the 


XXX11  EXPLANATION   OF   THE   TABLES. 

table.  Then  find  the  number  corresponding  to  this  difference 
and  multiply  it  by  the  power  of  10,  whose  logarithm  was 
subtracted  at  the  beginning.  Thus,  to  find  the  number  whose 
Napierian  logarithm  is  9.62983 : 

log  100  =  2  log  10  =  4.60517 

9.62983  —  4.60517  =  5.02466 

5.02466  is  the  logarithm  of  some  number  between  152  and  153. 
Given  log  =5.02466 

log  152  =5.02388 

difference  78 

tabular  difference  =       656 
78  -4-  656  =  .12. 

5.02466  is  the  logarithm  of  152.12. 
Hence,  9.62983  is  the  logarithm  of  152.12  X  100  =  15212. 


TABLE    I. 


COMMON   LOGARITHMS 
OF  NUMBERS. 


If. 

O 

l 

2 

3 

4 

5 

6    7 

8 

9 

Prop.  Pts. 

100 

00  000 

043 

087 

130 

173 

217 

260 

303 

346 

389 

01 

432 

475 

518 

561 

604 

647 

689 

732 

775 

817 

44 

43 

42 

02 
03 

860 

oi  284 

903 

326 

945 

368 

988 
410 

452 

*072 

494 

*ii5 
536 

*I57 
578 

*i99 
620 

*242 
662 

i 

2 

4.4 
8.8 

4-3 
8.6 

& 

04 

703 

745 

787 

828 

870 

912 

953 

995 

*o36 

*078 

3 

13.2 

I2.9 

12.6 

05 

02  119 

160 

202 

243 

284 

325 

366 

407 

449 

490 

4 

17.6 

17.2 

16.8 

06 

531 

572 

612 

653 

694 

735 

776 

816 

857 

898 

i 

22.  0 
26  A 

21.5 

21.0 

25.2 

07 
08 
09 

938 
03  342 

743 

979 
383 
782 

423 
822 

*o6o 

463 
862 

*IOO 

503 
902 

*i4i 

543 
941 

*i8i 

583 
981 

*222 
623 
*O2I 

*262 
663 

*o6o 

*3<>2 

703 

*IOO 

I 

9 

*v.«| 

30-8 

35-2 
39.6 

30.1 
38.7 

29.4 

33-6 
37.8 

110 

04  139 

179 

218 

258 

297 

336 

376 

415 

454 

493 

II 

532 

57  i 

610 

650 

689 

727 

766 

805 

*844 

*883 

41 

40 

39 

12 

922 

961 

999 

*o38 

*o77 

*II5 

*i54 

*I92 

i 

4.1 

4.0 

7.0 

13 

05  308 

346 

385 

423 

461 

500 

538 

576 

614 

652 

2 

8.2 

8.0 

O  :? 

7.8 

14 
15 

690 

06  070 

729 
108 

767 
145 

805 
183 

843 

221 

88l 

258 

918 
296 

956 

333 

994 

*032 
408 

3 
4 

12.3  12.0 

16.4  16.0 

ii.  7 
15-6 

16 

446 

483 

558 

595 

633 

670 

707 

744 

781 

5 

20.5 

20.  o 

19-5 

6 

24.6 

24.0 

23.4 

17 

819 

856 

893 

930 

967 

*oo4 

*o4  1 

^078 

*"5 

^151 

28.7 

28.0 

27.3 

18 

07  188 

225 

262 

298 

335 

372 

408 

445 

482 

518 

g 

•3.2.8 

72.  0 

31.2 

19 

555 

628 

664 

700 

737 

773 

809  |  846 

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835 
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276 
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567 

404 

553 
702 

850 

997 

144 

290 
436 
582 

419 
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159 

305 

451 
596 

434 
583 
731 
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173 

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465 
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449 
598 
746 

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188 

334 
480 

625 

464 

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202 

349 
494 
640 

479 
627 

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217 

363 
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232 

378 
524 
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657 
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246 

392 

538 
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3 
4 
5 
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727 

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770 

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2 

3 

4 

5 

6 

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8 

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0    1 

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116 

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302 

316 

330 

344 

359  373 

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401 

416 

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430 

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544 

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601 

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178 

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234 

248 

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276 

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346 

360 

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255 

268 

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295 

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322  335  348 

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375 

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402 

415 

428 

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27 

455  468 

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601 

614 

627 

640 

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257 

270 

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297 

310 

323 

336 

349 

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414 

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440 

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543 

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233 

245 

258 

270 

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283 

295 

307 

320 

332 

345 

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5 

6 

7 

8 

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432 

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55 
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58 
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267 
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543 
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157 

279 
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047 
169 

291 
413 

534 

568 
691 
814 

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060 
182 

303 
425 
546 

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704 

827 

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194 

315 
437 
558 

593 
716 

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206 

328 
449 
570 

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728 
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218 

340 
461 
582 

617 

741 
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108 
230 

352 
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630 

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121 
242 

364 
485 
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642 

765 
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255 

376 
497 
618 

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3 
4 
5 
6 

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715 

727 

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241 
360 

478 

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253 
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73 

74 
75 
76 

77 
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299 

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83 
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670 

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115 
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127 
240 
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580 
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93 

94 
95 
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439 

550 
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251 

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400 

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p.  Pts. 

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4 

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6 

7 

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963 

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091 

155 
219 

711 

776 
840 

905 
969 
*o33 

097 
161 
225 

718 
782 
847 

911 
*975 

104 
168 
232 

724 
789 
853 
918 
982 

no 
174 
238 

730 
795 

924 

*f2 

117 
181 
245 

251 

315 

378 
442 

506 
569 
632 

696 

759 
822 

257 

264 

270 

276 

283 

289 

296 

302 

308 

321 
385 
448 

512 
575 
639 
702 

765 
828 

327 
391 

455 

582 
645 

708 

771 
835 

334 
3f 
461 

525 

651 

715 
778 
841 

340 
404 
467 

531 

594 
658 

721 

784 
847 

347 
410 

474 

537 
601 
664 

727 
790 

853 

353 
417 
480 

544 
607 
670 

734 
797 
860 

359 
423 
487 

550 
613 
677 

740 

i 

366 
429 
493 

556 
620 
683 

746 
809 

872 

372 
436 
499 

563 
626 
689 

753 
816 

879 

885 

891 

897 

904 

910 

916 

923 

929 

935 

942 

948 
84  on 
073 

136 
198 
261 

323 

386 
448 

954 
017 
080 

142 
205 
267 

330 
392 
454 

960 
023 
086 

148 

211 
273 

336 
398 
460 

967 
029 
092 

155 
217 
280 

342 
404 
466 

973 
036 
098 

161 
223 
286 

348 
410 

473 

979 

042 

105 

167 
230 
292 

354 
417 
479 

985 
048 
in 

173 
236 
298 

423 
485 

992 
055 
117 

180 
242 
305 

367 
429 
491 

998 
061 
123 

186 
248 
311 

373 
435 
497 

067 
130 

192 

255 
317 

379 
442 
504 

5io 

5i6 

522 

528 

535 

54i 

547 

553 

559 

566 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

N. 

0 

1 

2 

\  3 

4 

5 

6 

7 

8 

9 

Pro 

).  Pts. 

700 

84  510 

5i6 

522 

528 

535 

541 

547 

553 

559 

566 

01 

02 
03 
04 

05 
06 

07 
08 
09 

572 
634 
696 

757 
819 
880 

942 

85  003 
065 

578 
640 
702 

763 
825 
887 

948 
009 
071 

584 
646 
708 

770 

831 
893 

954 
016 
077 

590 
652 
7H 
776 
837 
899 
960 
022 
083 

597 
658 
720 

782 
844 
905 

967 
028 
089 

603 
665 
726 

788 
850 
911 

973 
034 
095 

609 
671 
733 

794 
856 
917 

979 
040 

101 

615 
677 
739 
800 
862 
924 

985 
046 
.107 

621 
683 
745 

807 
868 
930 
991 
052 
114 

628 
689 

751 

813 
874 
936 

997 
058 

120 

I 

2 

3 

7 

0.7 
1.4 

2.1 

710 

126 

132 

138 

144 

150 

156 

163 

169 

175 

181 

4 

2.8 

•7  C 

ii 

12 
13 

14 
15 

16 

17 
18 

19 

187 
248 
309 
37o 
43i 
491 

552 
612 

673 

193 
254 
3i5 

376 
437 
497 

558 
618 
679 

199 
260 

321 

382 
443 
503 

564 
625 
685 

205 
266 
327 
388 
449 
509 

570 

63i 
691 

211 
272 

333 

394 
455 
5i6 

576 
637 
697 

217 
278 
339 
400 
461 
522 

582 
643 
703 

224 

285 
345 
406 
467 
528 

588 
649 
709 

230 
291 

352 
412 
473 
534 

594 
655 
715 

236 
297 
358 

418 

479 
540 

600 
661 
721 

242 

303 
364 

425 

485 
546 

606 

667 
727 

6 
9 

O'O 

4-2 

4-9 
5-6 
6-3 

720 

733 

739 

745 

75i 

757 

763 

769 

775 

78i 

788 

21 
22 
23 

24 
25 
26 

27 
28 
29 

794 
854 
9M 

974 
86  034 
094 

153 
213 

273 

800 
860 
920 

980 
040 

100 

159 
219 

279 

806 
866 
926 

986 
046 
106 

165 
225 
285 

812 
872 
932 

992 
052 

112 

171 
231 
291 

818 
878 
938 

998 
058 
118 

177 
237 
297 

824 
884 
944 
*oo4 
064 
124 

183 
243 
303 

830 
890 
950 

*OIO 

070 
130 

189 

249 
308 

836 
896 
956 

*oi6 
076 
136 

195 

255 
3H 

842 
902 
962 

*O22 
082 
141 

201 
26l 
320 

848 
908 
968 

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088 
147 
207 

267 
326 

*  i 

2 

3 

4 

1 

8 
9 

6 

0.6 

1.2 

1.8 
2.4 
3-0 
3-6 

4-2 

4.8 

5-4 

730 

332 

338 

344 

350 

356 

362 

368 

374 

380 

386 

3i 
32 
33 

34 
35 
36 

37 
38 
39 

392 
45i 
5io 

570 
629 
688 

747 
806 
864 

398 
457 
5i6 

576 
635 
694 

753 
812 
870 

404 

463 
522 

58i 
641 
700 

759 
817 
876 

410 
469 
528 

587 
646 

705 

764 
823 
882 

4i5 

475 
534 

593 
652 
711 

770 

421 

481 
540 

717 

776 
835 
894 

427 

487 

546 

605 
664 
723 
782 
841 
900 

433 
493 
552 

611 
670 
729 
738 
847 
906 

439 

499 
558 

617 
676 

735 

794 
853 
911 

445 
504 
564 

623 
682 
74i 
800 

859 
917 

i 

2 

3 

5 

0-5 

I.O 

i-5 

740 

923 

929 

935 

941 

947 

953 

958 

964 

970 

976 

4 

2.0 

4i 
42 
43 

44 
45 
46 

47 
48 

49 

982 

87  040 
099 

157 
216 

274 

332 
390 
448 

988 
046 
105 
163 

221 
280 

338 
396 

454 

994 

052 
in 

169 
227 
286 

344 
402 
460 

999 

058 
116 

175 
233 
291 

349 
408 
466 

*oo5 
064 

122 

181 

239 
297 

355 
413 
47i 

*OI  I 

070 
128 

186 
245 
303 

36i 
419 

477 

*oi7 
075 
134 
192 
251 
309 

367 
425 
483 

*023 

081 
140 

198 
256 
315 

373 

$ 

*029 

087 

146 

204 
262 
320 

379 
437 
495 

*o35 
093 
151 

210 
268 
326 

384 
442 
500 

9 

2.5 

3-0 
3-5 
4.0 

4-5 

750 

506 

5" 

5i8 

523 

529 

535 

54i 

547 

552 

558 

N. 

0 

1 

•z 

:* 

t 

5 

6 

7 

N 

9 

I'roi 

).  I'tS. 

N. 

O    1    2    3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

750 

5i 
52 
53 

54 
55 
56 

11 

59 
760 

61 
62 
63 
64 
65 
66 

6? 
68 
69 
770 

7i 
72 
73 

74 
75 
76 

77 
78 
79 
780 
81 
82 
83 

84 
85 
86 

87 
88 
89 
790 

9i 
92 

93 

94 
95 
96 

97 
98 
99 
800 

87  506 

512 

5i8 

523 

529 

535 

541 

547 

552 

558 

I 

2 

3 
4 

6 

8 
9 

i 

2 

3 
4 
5 
6 

8 
9 

6 
0.6 

1.2 

1.8 
2.4 
3-0 
3-6 
4.2 
4-8 
54 

5 

o.5 

I.O 

1.5 

2.0 
2-5 

3-0 
3-5 
4.0 

4-5 

564 
622 
679 

737 
795 
852 

910 
967 
88  024 

570 
628 
685 

743 

800 
858 

915 
973 
030 

576 
633 
691 

749 
806 
864 

921 

978 
036 

58i 
639 
697 

754 
812 
869 

927 

984 
041 

587 
645 
703 

760 
818 
875 

933 
990 

047 

593 
651 
708 

766 
823 
881 

938 
996 

053 

599 
656 

714 

772 
829 
887 

944 

*OOI 

058 

604 
662 
720 

777 
835 
892 

950 
*oo7 
064 

610 
668 
726 

783 
841 
898 

955 

*OI3 

070 

616 

674 
73i 

789 
846 
904 

961 

*oi8 
076 

081 

087 

093 

098 

104 

no 

116 

121 

127 

133 

138 
195 
252 

309 
366 
423 
480 
536 
593 

144 

201 

258 

315 
372 
429 

485 
542 
598 

150 
207 
264 

321 
377 
434 

491 

547 
604 

156 
213 
270 

326 

383 
440 

497 
553 
610 

161 
218 
275 

332 
389 
446 

502 
559 
615 

167 
224 
281 

338 
395 
45i 

508 

564 
621 

173 
230 

287 

343 
400 

457 

513 
570 
627 

I78 

235 
292 

349 
406 

463 

519 
576 
632 

184 
241 
298 

355 
412 
468 

525 
58i 
638 

190 
247 
304 

360 

417 
474 

530 

587 
643 

649 

655 

660 

666 

672 

677 

683 

689 

694 

700 

705 
762 
818 

874 
930 
986 

89  042 
098 
154 

711 
767 
824 

880 
936 
992 

048 
IO4 
159 

717 

773 
829 

885 
941 
997 

053 
109 

165 

722 

779 
835 
891 

947 
*oo3 

059 
H5 
170 

728 

784 
840 

897 
953 

*009 

064 

120 
176 

734 
790 
846 

902 

958 
*oi4 

070 
126 
182 

739 
795 
852 

908 
964 

*020 
076 

I3I 

187 

745 
801 

857 

913 
969 

*025 

081 
137 
193 

750 
807 
863 

919 

975 
*o3i 

087 
198 

756 
812 
868 

925 
981 
*o37 

092 
148 
204 

209 

215 

221 

226 

232 

237 

243 

248 

254 

260 

265 
321 
376 

432 
487 
542 

597 
653 

708 

271 
326 

382 

437 
492 
548 

603 
658 
713 

276 

443 
498 
553 
609 
664 
719 

282 
337 
393 

448 
504 
559 

614 
669 
724 

287 

343 
398 

454 
509 
564 
620 
675 
73° 

348 
404 

459 
515 
57o 

625 
680 

735 

298 

354 
409 

465 
520 
575 

631 
686 
741 

304 
360 
415 
470 
526 
58i 

636 
691 
746 

310 

365 
421 

476 

531 
586 

642 
697 
752 

315 
37i 
426 

481 
537 
592 

647 
702 

757 

763 

768 

774 

779 

785 

79° 

796 

801 

807 

812 

818 
873 
927 

982 
90  037 
091 

146 
200 
255 

823 
878 
933 

988 
042 
097 

151 
206 
260 

829 
883 
938 

993 

048 

102 

157 
211 
266 

834 
889 
944 

998 
053 
108 

162 
217 
271 

840 
894 
949 
*oo4 
059 
"3 
168 

222 

276 

845 
900 

955 
*oo9 
064 
119 

173 

227 
282 

851 
905 
960 

-015 
069 
124 

179 

233 
287 

856 
911 
966 

*O2O 

075 
I29 

184 
238 
293 

862 
916 
971 

*026 

080 

135 
189 

244 

298 

867 
922 
977 

*03I 

086 
140 

*95 
249 
304 

309 

3i4 

320 

325 

331 

336 

342 

347 

352 

358 

N. 

0    1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

i6 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Pro] 

[>.  PtS. 

800 

90  309 

314 

320 

325 

331 

336 

342 

347 

352 

358 

OI 
02 
03 
04 

05 
06 

07 
08 
09 

363 
417 
472 

526 

634 
687 
741 
795 

369 

423 
477 

585 
639 

693 
747 
800 

374 
428 
482 

536 
590 
644 

698 
752 
806 

380 
434 
488 

542 
596 
650 

703 
757 
811 

385 
439 
493 

547 
601 

655 

709 

763 
816 

39° 

445 
499 

553 
607 
660 

768 
822 

396 
450 
504 

558 
612 
666 

720 

773 
827 

401 
455 
509 

563 
6i7 
671 

725 
779 
832 

407 
461 
515 

569 
623 
677 

730 
784 
838 

412 
466 
520 

574 
628 
682 

736 

789 
843 

810 

849 

854 

859 

865 

870 

875 

881 

886 

891 

897 

ii 

12 

14 

II 

17 

18 
19 

902 
956 
91  009 

062 
116 
169 

222 

275 
328 

907 
961 
014 

068 

121 
174 

228 

28l 

334 

020 

% 

180 
339 

918 
972 
025 

078 
132 
185 

238 
291 

344 

924 
977 
030 

084 

137 
190 

243 
297 

350 

929 
982 
036 

089 
142 
196 

249 
302 

355 

041 

094 
148 

201 

254 
307 
360 

940 

993 
046 

100 

153 
206 

259 
312 
365 

945 
998 
052 

105 

158 

212 

265 

318 
371 

950 
*oo4 

057 

1  10 

164 
217 

270 
323 
376 

I 

2 

3 
4 

6 
8 

6 

0.6 

1.2 

1.8 

2.4 

3-o 
3-6 

4-2 

4-8 

820 

381 

387 

392 

397 

403 

408 

413 

418 

424 

429 

9 

5-4 

21 
22 
23 

24 
25 
26 

27 
28 
29 

434 
487 

593 

803 
855 

440 
492 
545 

598 
651 
703 

756 
808 
861 

445 
498 

603 
656 
709 

761 
814 
866 

450 

609 
66  1 

714 

766 
819 
871 

614 
666 
719 

772 
824 
876 

461 
514 
566 

619 
672 
724 

777 
829 
882 

466 

519 
572 

624 
677 
730 
782 
834 
887 

47i 
524 
577 
630 
682 
735 

787 
840 
892 

477 
529 
582 

635 
687 
740 

793 
845 
897 

482 
535 

640 
693 
745 

798 
850 
903 

880 

908 

913 

918 

924 

929 

934 

939 

944 

950 

955 

32 
33 

34 

37 
38 
39 

960 

92  OI2 
065 

117 
169 
221 

273 
324 
376 

965 
018 
070 

122 

174 
226 

278 
330 
381 

971 
023 
075 
127 
179 
231 

283 
335 
387 

976 
028 
080 

132 
184 
236 

288 
340 
392 

981 

033 
085 

137 
189 
241 

293 
345 
397 

986 
038 
091 

143 
195 

247 

298 
350 
402 

991 
044 
096 

148 
200 
252 

304 
355 
407, 

997 

049 

101 

153 
205 

257 
309 
412 

*002 
054 

106 
158 

210 
262 

366 
4l8 

*oo7 

059 
in 

163 
215 
267 

319 

37i 
423 

i 

2 

3 
4 
5 
6 

7 

5 

I.O 

i-5 

2.0 
2.5 
3-0 
3-5 

840 

428 

433 

438 

443 

449 

454 

459 

464 

469 

474 

8 

4.0 

'  42 
43 

44 
45 
46 

47 
48 
49 

480 
531 
583 

634 

686 
737 

788 
840 
891 

s 

588 

639 
691 
742 

793 

490 

542 
593 
645 

747 

799 
850 
901 

495 

547 
598 

650 
701 
752 

8°- 

500 

655 
706 

758 

809 
860 
911 

505 

557 
609 

660 
711 
763 
814 
865 
916 

5" 

562 
614 

665 
716 
768 

819 
870 
921 

567 
619 

670 
722 

773 
824 

875 
927 

521 

572 
624 

675 
727 
778 
829 

881 
932 

526 

578 
629 

681 
732 
783 

834 
886 

937 

9 

4-5 

850 

942 

947 

952 

957 

962 

967 

973 

978 

983 

988 

N. 

0 

1 

2 

3 

I 

I 

; 

7 

8 

» 

Pro] 

).  PtS. 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Pro 

p.  Pts. 

850 

92  942 

947 

952 

957 

962 

967 

973 

978 

983 

988 

5i 
52 
53 

54 
55 
56 

57 
58 
59 

993 
93  044 
095 
146 
197 
247 
298 
349 
399 

998 
049 

IOO 

151 

202 
252 

303 

354 
404 

*oo3 
054 
105 

156 
207 
258 
308 

359 
409 

*oo8 

059 
no 

161 

212 
263 

313 
364 
414 

*oi3 
064 
H5 
166 
217 
268 

3i8 
369 
420 

"018 
069 

120 

171 
222 
273 
323 

374 
425 

*024 

075 
125 

176 

227 
278 

328 
379 
430 

*029 

080 
I31 
181 
232 
283 

334 
384 
435 

*034 

s 

1  86 

237 
288 

339 

389 
440 

*039 
090 
141 

192 
242 
293 

344 
394 
445 

i 

2 

3 

6 

0.6 

1.2 

1.8 

860 

450 

455 

460 

465 

470 

475 

480 

485 

490 

495 

4 
5 

2.4 

•7  O 

61 
62 
63 
64 

65 
66 

67 
68 
69 

500 

55i 
601 

651 
702 

752 
802 
852 
902 

505 
556 
606 

656 
707 
757 
807 

857 
907 

5io 

56i 
611 

661 
712 
762 

812 
862 
912 

515 
566 

616 

666 
717 
767 

817 
867 
917 

520 

57i 
621 

671 
722 

772 

822 
872 
922 

526 
576 
626 

676 
727 

777 
827 
877 
927 

53i 
58i 
631 
682 
732 
782 

832 
882 
932 

536 
586 
636 

687 

737 
787 

837 
887 
937 

54i 
59i 
641 

692 

742 
792 

842 
892 
942 

546 
596 
646 

697 

747 
797 

847 
897 
947 

6 

1 

9 

1.6 

4.2 

4.8 
5-4 

870 

952 

957 

962 

967 

972 

977 

982 

987 

992 

997 

7i 
72 

73 

74 
75 
76 

77 
78 
79 

94  002 
052 

101 

151 

201 
250 

300 

349 
399 

007 

057 
106 

156 
206 
255 

305 
354 
404 

012 
062 
III 

161 

211 
260 

310 

359 
409 

017 
067 
116 

166 
216 
265 

315 
364 

414 

022 
072 
121 

171 
221 
270 

320 

369 
419 

027 
077 
126 

176 
226 
275 

325 

374 
424 

082 
131 
181 
231 
280 

330 
379 
429 

037 
086 

136 
186 
236 
285 

384 
433 

042 
091 
141 

191 
240 
290 

34o 

047 
096 
146 

196 
245 
295 

345 
394 
443 

i 

2 

3 
4 
5 
6 

8 
9 

5 

0.5 

I.O 

i-5 

•2.O 
2-5 

3.0 

3-5 

4.0 

4-5 

880 

448 

453 

458 

463 

468 

473 

478 

483 

488 

493 

81 
82 
83 
84 
85 
86 

87 
88 
89 

498 
547 
596 

645 
694 

743 

792 
841 
890 

503 
552 
601 

650 

797 
846 

895 

507 
557 
606 

655 
704 

753 
802 

851 
900 

512 
562 
611 

660 

709 
758 

807 
856 
905 

517 
567 

616 

665 
714 
763 
812 
861 
910 

522 

57i 
621 

670 
719 
768 

817 
866 
9*5 

527 
576 
626 

675 

724 
773 
822 
871 
919 

532 
58i 
630 

680 
729 
778 

827 
876 
924 

537 
586 

635 
685 

734 
783 

832 
880 
929 

542 

59i 
640 

689 
738 
787 
836 
885 
934 

i 

2 

3 

4 

0.4 
0.8 

1.2 

890 

939 

944 

949 

954 

959 

963 

968 

973 

978 

983 

4 

1.6 

91 
92 

93 

94 
95 
96 

97 
98 

99 

988 
95  036 
085 

134 

182 
231 

279 
328 
376 

993 
041 
090 

139 
187 
236 

284 
332 

38i 

998 
046 
095 

143 
192 

240 

289 

337 
386 

*002 

051 

IOO 

148 
197 
245 

294 

342 

39° 

*007 

056 
105 
153 

202 
250 

299 

347 
395 

*OI2 

061 

109 
158 

207 
255 

303 
352 

400 

*oi7 
066 
114 

163 

211 
260 

308 

357 
405 

*022 

071 
119 

168 
216 
265 

313 
36i 
410 

*027 

075 
124 

173 
221 
270 

318 
366 
415 

*032 

080 
129 

177 
226 
274 

323 
371 
419 

6 

8 
9 

2.O 

2-4 
2.8 

11 

900 

424 

429 

434 

439 

444 

448 

453 

458 

463 

468 

N. 

O 

1 

* 

3 

4 

5 

6 

7 

8 

9 

Proj 

>.  Pts. 

i8 


w. 

0123 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

900 

01 

02 
03 
04 

05 
06 

07 
08 
09 
910 
ii 

12 
13 

14 
15 

16 

17 
18 

920 

21 
22 
23 
24 

25 
26 

27 
28 
29 

930 

32 
33 

34 
35 
36 

37 
38 
39 
940 

42 
43 

44 
45 
46 

47 
48 
49 
950 

95  424 

429 

434 

439 

444 

448 

453 

458 

.463 

468 

I 

2 

3 

4 

6 

8 
9 

i 

2 

3 
4 

6 

8 
9 

5 

0-5 

I.O 

1-5 

2.0 
2-5 

3-o 

3.5 
4.0 

4.5 

4 

0.4 
0.8 

1.2 

1.6 

2.O 

2-4 
2.8 

3-2 
3-6 

472 
521 
569 

617 
665 
713 

76i 

809 
856 

477 
525 
574 

622 
670 
718 

766 

813 
86  1 

482 
530 
578 

626 
674 
722 

770 
818 
866 

437 
535 
583 

679 
727 

775 
823 
871 

492 
540 
588 

636 
684 
732 

780 

828 
875 

497 
545 
593 
641 
689 
737 

785 
832 
880 

SGI 
550 
598 

646 
694 
742 

789 

837 
885 

506 

650 
698 
746 

794 
842 
890 

559 
607 

655 
703 
751 

799 
847 
895 

516 
564 
612 

660 

708 
756 
804 
852 
899 

904 

909 

914 

918 

923 

928 

933 

938 

942 

947 

952 
999 
96  047 

095 
142 
190 

237 
284 
332 

957 

*OQ4 

052 

099 
147 
194 

242 
289 
336 

961 

*oc>9 
057 
104 
152 
199 

246 
294 

06  1 

109 
156 
204 

251 
298 
346 

066 

114 
161 
209 

256 
303 
350 

976 

*023 
071 

118 
166 

213 

261 

308 
355 

980 

*028 

076 

123 
171 

218 

265 

313 
360 

*985 
*o8o 

128 

175 
223 

270 
317 
365 

990 

*o38 
085 

133 
180 
227 

275 
322 
369 

*o9! 
090 

137 
185 
232 

280 
327 
374 

_379_ 
426 

473 
520 

'   614 
661 

708 

755 
802 

384 

388 

393 

398 

402 

407 

412 

417 

421 

43i 

478 

525 

572 
619 
666 

713 
759 

435 
483 
530 

577 
624 
670 

717 
764 
811 

440 
487 
534 

58i 
628 
675 

722 
769 
816 

445 
492 
539 
586 

633 
680 

727 
774 
820 

450 
497 

544 

638 
685 

778 
825 

454 
501 
548 

595 
642 
689 

736 
783 
830 

459 
506 

553 

600 
647 
694 

741 

788 

834 

464 

558 

605 
652 
699 

745 
792 
839 

468 

515 
562 

609 
656 
703 

750 
797 
844 

848 

853 

858 

862 

867 

872 

876 

881 

886 

890 

895 
942 

988 

97  035 
08  1 
1*8 

220 
267 

900 
946 
993 

039 
086 

132 

179 
225 
271 

904 
95i 
997 
044 
090 
137 

183 
230 
276 

909 
956 

*002 
049 

095 
142 

188 

234 
280 

914 
960 
*oo7 

053 

IOO 

146 
192 

239 
285 

918 
965 

*OII 

058 
104 
151 
197 

243 

290 

923 
970 
*oi6 

063 
109 
155 
202 
248 
294 

928 

974 

*02I 

067 
114 

160 
206 
253 
299 

932 

*979 

072 
118 
165 

211 
257 
304 

937 
*984 

077 
123 
169 

216 
262 
308 

_3Jf3_ 

359 

405 
45i 

497 
543 
589 

727 

317 

322 

327 

331 

336 

340 

345 

350 

354 

364 
410 
456 
502 
548 
594 
640 
685 

368 
414 
460 

506 

552 
598 

644 
690 
736 

373 
419 

465 

557 
603 

649 
695 
740 

377 
424 
470 

607 

§9 
745 
791" 

382 
428 
474 

520 
566 
612 

658 
704 
749 

387 
433 
479 

525 

617 

663 
708 
754 

391 
437 
483 

529 
575 
621 

667 

759 

396 

442 
488 

534 
580 
626 

672 

717 

400 

447 
493 

539 

630 

676 
722 

772 

777 

7*2 

786 

Soo 

804 

809 

813 

N. 

0    1 

2   :j   i 

5    0 

7 

8    0 

Proi 

..  Pis. 

N. 

o 

1 

2 

3    4 

5 

6  |  7 

8 

9 

Prop.  Pts. 

950 

5i 
52 
53 

-  54 
55 
56 

57 
58 
59 
OGO 
61 
62 
63 
64 

65 
66 

67 
68 
69 
970 

7i 
72 

73 

74 
75 
76 

11 

79 
980 

81 
82 
83 

84 
85 
86 

87 
88 
89 
990 

9i 
92 
93 

94 
95 
96 

.97 
98 

99 
1000 

97  772 

777 

782 

786 

791 

795 

800 

804 

809 

8i3 

i 

2 

3 
4 
5 
6 

9 

i 

2 

3 
4 
5 
6 

8 
9 

5 

0.5 

I.O 

i-5 

2.0 
2-5 

3-o 
3-5 

4.0 

4-5 

4 

0.4 
0.8 

1.2 

1.6 

2.0 
2.4 
2.8 

% 

818 
864 
909 

955 
98  ooo 
046 

091 

137 
182 

823 
868 
914 

959 
005 
050 

096 
141 

186 

827 

873 
918 

964 
009 
055 

100 

146 
191 

832 
877 
923 

968 
014 

059 

105 
150 
195 

836 
882 
928 

973 
019 
064 

109 
155 

200 

841 
886 
932 

978 
023 

068 

114 

159 

204 

845 
891 

937 
982 
028 
073 
118 
164 
209 

850 
896 
941 

987 
032 
078 

123 
1  68 
214 

855 
900 
946 

991 

037 
082 

127 

173 
218 

859 
9°5 
950 

996 

041 
087 

132 

177 
223 

227 

232 

236 

241 

245 

250 

254 

259 

263 

268 

272 
3i8 
363 
408 
453 
498 

543 
588 
632 

277 
322 

367 
412 

457 
502 

547 
592 
637 

281 
327 

372 

417 
462 

507 
552 
597 
641 

286 
331 
376 

421 
466 
5ii 

556 
601 
646 

290 
336 
381 

426 
471 
516 

561 
605 
650 

295 
340 
385 

430 
475 
520 

565 
610 

655 

299 
345 
390 

435 

480 

525 

57o 
614 

659 

3°4 
349 
394 

439 
484 
529 

574 
619 
664 

308 
354 
399 

444 
489 

534 

579 
623 
668 

313 
358 
403 

448 
493 
538 

583 
628 

673 

677 

682 

686 

691 

695 

700 

704 

709 

713 

717 

722 
767 
8x1 

856 
900 
945 

989 
99  034 
078 

726 
771 
816 

860 
9°5 
949 

994 

038 
083 

73i 
776 
820 

865 
909 
954 
998 
043 
087 

825 

869 
914 
958 

-003 
047 
092 

740 
784 
829 

874 
9l8 

963 
*007 

052 

096 

744 
789 
834 
878 

923 
967 

*OI2 
056 
100 

749 
793 
838 

883 
927 
972 

*oi6 
061 
105 

753 
798 

843 
887 
932 
976 

*02I 
065 
I09 

758 
802 
847 

892 
936 
981 

*025 

069 

114 

762 
807 
851 
896 
941 
985 

*029 

074 

118 

123 

127  131 

136 

140 

145 

149 

154 

158 

162 

167 

211 
255 
300 

344 
388 

432 
476 
520 

171 
216 
260 

304 
348 
392 

436 
480 
524 

176 

220 
264 

308 
352 
396 
441 

484 
528 

180 
224 
269 

313 

357 
401 

445 
489 
533 

185 

229 
273 

317 
361 

405 

449 
493 
537 

I89 

233 
277 

322 

366 
410 

454 
498 
542 

193 

238 
282 

326 
370 
414 

458 
502 
546 

I98 
242 
286 

330 

374 
419 

463 
506 
550 

202 
247 
291 

335 
379 
423 
467 
5u 
555 

207 
251 
295 

427 
471 
515 
559 

564 

568 

572 

577 

58i 

585 

590 

594 

599 

603 

607 
651 
695 

739 
782 
826 

870 
913 
957 

612 
656 
699 

743 

787 
830 

874 
917 
961 

616 
660 

704 

747 
791 

835 

878 
922 
965 

621 

664 
708 

752 
795 
839 

883 
926 
970 

625 
669 
712 

756 
800 

843 
887 
930 
974 

629 

673 
717 

760 

804 
848 

891 

935 

978 

634 
677 
721 

765 
808 
852 
896 
939 
983 

638 
682 
726 

769 

813 
856 

900 

944 

987 

642 
686 
730 

774 
817 
861 

904 
948 
991 

647 
691 

734 

778 
822 
865 

909 
952 
996 

00  000 

004 

009 

013 

017 

022 

026 

030 

035 

039 

N.  , 

O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

20 


TABLE    II. 

CONSTANTS  WITH  THEIR  LOGARITHMS. 

Number. 

Logarithm. 

TT  (ratio  of  circumference  to  diameter)  .   .   . 

7T2           ... 

3.14159265 
9.86960440 
1.77245385 
0.31830989 

O.IOI32II8 
0.56418958 

3600 
2i6oo/ 
I  296000" 

57°.2957795 
3437^74677 
206264".  806 

.01745329 
.00029089 
.000004848 

2.718281828 
0.434294482 

3.8197186 

3963.296 
3949.790 
3956. 

39-37 
39.37079 

39.37043 
5280. 
6080.290 

1.466667 
0.681818 

0.49714  99 
0.99429  97 
0.24857  49 

9.50285  01  —  10 
9.00570  03  —  10 
9.75142  51—10 

2.55630  25 
4-33445  38 
6.11260  50 

1.75812  26 

3-53627  39 
5.31442  51 

8.24187  74  —  10 
6.46372  61  —  10 
4.68557  49—10 

0.43429  45 
9.63778  43—10 

0.58203  14 

3-59805  65 
3-59657  4o 
3.59725  63 

i.595i6  54 
I.595I7  4i 
I.595I7  oi 
3.72263  39 
3-78392  43 

.16633  15 
9.83366  86—10 

V*   

I 

I 

I 

v«  '  

Number  of  degrees  in  circumference  .... 
minutes                              .... 
seconds               "              .... 

Degrees  in  arc  equal  to  radius  . 

Minutes        "       "             "          .... 

Seconds       "       "             "          

Length  of  arc  of  i  degree  

"             "        i  minute  

"             "        i  second     

Napierian  base  

Modulus  of  common  logarithms  .               .    . 

Hours  in  which  earth  revolves  through  arc 
equal  to  radius  

Equat.  radius  of  earth,  miles  (Clarke,  1878) 
Polar         "             "         "             "          " 
Mean        "             "         "        

Inches  in  i  metre  (U.  S.  Standard)  
"         i      "      (British  Standard)    .... 
"         i      "      (Clarke   1866) 

Feet  in  i  mile     .   .       .... 

Feet  in  i  nautical  mile  (U.  S.  Coast  Survey) 
Feet  per  second  in  i  mile  per  hour 

Miles  per  hour  in  i  foot  per  second    .... 

21 


TABLE    III. 


LOGARITHMS 


OF  THE 


SINE,  COSINE,  TANGENT,  AND  COTANGENT 


EACH   MINUTE  OF   THE   QUADRANT. 


22 


r 

L.  Sin. 

d. 

L.Tarig.  c.  d.  L.Cotg. 

L.  Cos. 

Prop.  Pts. 

O 

i 

2 

3 
4 

6.46  373 
6.76  476 
6.94  085 
7.06  579 

30103 
17609 
12494 
9691 
7918 
6694 
5800 
5"5 
4576 

4*39 
3779 
3476 
3218 

6.46  373 
6.76  476 
6.94  085 
7.06  579 

30103 
17609 
12494 
9691 
7918 
6694 
5800 

5"5 
4576 
4139 
3779 
3476 
3219 
2996 
2803 
2633 
2482 
2348 
2228 
2119 

2O2O 

J93i 
1848 

1773 
1704 
1639 
1579 

*524 

1473 
1424 
1379 
1336 
1297 

"59 
1223 
1190 

"59 
1128 

IIOO 

1072 
1047 

1022 
998 
976 

955 
934 
9^5 
895 
878 

860 

843 
828 
812 
797 
782 
769 
756 
742 
73<> 

3-53  627 
3-23  524 
3-05  915 
2.93  421 

o.oo  ooo 

0.00  000 

o.oo  ooo 

0.00  000 

o.oo  ooo 

6O 

59 
58 
57 
56 

d. 

I336 
1297 

1259 
1223 
1190 
"59 
1158 
1128 

IIOO 

1072 
1047 
1046 

IO22 

999 
998 
976 
955 
954 
934 

d. 

30103 
17609 
12494 
9691 
7918 
6694 
5800 
5"5 
4576 
4139 
3779 
3476 
3219 
3218 

2997 
2996 
2803 
2802 

2633 
2483 
2482 
2348 
2228 
2227 
2119 

3021 
2020 

1931 

1930 
1848 

1773 
1704 
1639 
1579 
1524 
1473 
1472 
1424 
1379 

p.p.1" 
22.27 
21.62 
20.98 
20.38 
19.83 
19.32 
19.30 
18.80 
18.33 
17.87 
17.45 
17-43 
17.03 
16.65 
16.63 
16.27 
15-92 
15.90 
15-57 

p.p.l 
501.7 
293-4 
208.^ 
l6i.e 

I3I.9 
111.5 
96.6 
85-2 
76.2 
68.9 
62.9 
57-9 
53.^ 
53-^ 
49-9 
49-9 
46.7 
46.7 
43-8 
41.3 
41-3 
39-1 
37-1 
37-1 
35-3 
33-^ 
33^ 
32.1 
32.1 
30.8 
29.= 
28.4 
27-3 
26.3 
25.4 
24-5 
24-5 
23-7 
22.9 

d. 

9i5 
914 
896 

895 
878 
877 
860 

843 
828 
827 
812 
797 
782 
769 
756 
755 
743 
742 

73° 

2 

8 
3 

2 

7 
7 
7 
5 
7 
8 
8 
3 
5 
3 
5 
3 

2 
O 

8 
8 
7 
3 
3 

2 
2 

8 
7 
8 

7 

0 

5 
o 

2 
2 
0 

5 
3 
3 
8 

P-P-1" 
15-25 
15-23 
14-93 
14.92 

14-63 
14.62 

14-33 
14-05 
13.80 
13-78 
13-53 
13.28 
13-03 
12.82 
12.60 
12.58 
12.38 
12.37 
12.17 

6 

7 

8 

9 

7.16  270 
7.24  188 
7.30  882 
7.36  682 
7.41  797 

7.16  270 
7.24  188 
7.30  882 
7.36  682 
7.41  797 

2.83  730 
2.75  812 
2.69  118 
2.63  318 
2.58  203 

0.00  000 

o.oo  ooo 

0.00  000 

o.oo  ooo 

0.00  000 

55 
54 
53 
52 
5i 

10 

ii 

12 
13 
14 

7-46  373 
7-50  512 
7-54  291 
7-57  707 
7.60  985 

7-46  373 
7-50  512 
7-54  291 
7-57  767 
7.60  986 

2.53  627 
2.49  488 
2.45  709 
2.42  233 
2.39  014 

o.oo  ooo 
o.oo  ooo 

0.00  000 

o.oo  ooo 

0.00  000 

50 

49 
48 
47 
46 

15 

16 

17 

18 
19 

7.63  982 
7.66  784 
7.69  417 
7.71  900 
7-74  248 

2802 
2633 

2483 
2348 

7.63  982 
7.66  785 
7.69  418 
7.71  900 
7-74  248 

2.36  018 

2-33  215 
2.30  582 
2.28  100 

2.25  752 

0.00  000 

o.oo  ooo 
9-99  999 
9-99  999 
9-99  999 

45 
44 
43 

42 

4i 

20 

21 
22 
23 
24 

7.76  475 
7.78  594 
7.80  615 
7-82  545 
7-84  393 

2119 
202  1 
*93o 
1848 
1773 
1704 
1639 
J579 
1524 
1472 

1424 

1379 
1336 
1297 

.7.76  476 
7-78  595 
7.80  615 
7-82  546 
7-84  394 

2.23  524 

2.21  405 
2.19  385 

2.17  454 
2.15  606 

9-99  999 
9-99  999 
9-99  999 
9-99  999 
9-99  999 

40 

39 
38 
37 
36 

25 
26 
27 
28 
29 

7.86  166 
7.87  870 
7.89  509 
7.91  088 
7.92  612 

7.86  167 
7.87  871 
7-89  510 
7.91  089 
7.92  613 

2.13  833 

2.12  129 
2.IO  490 
2.08  911 
2.07  387 

9.99  999 
9-99  999 
9-99  999 
9-99  999 
9-99  998 

35 
34 
33 
32 
3i 

30 

3i 

32 
33 
34 

7-94  084 
7-95  508 
7.96  887 
7.98  223 
7-99  520 

7.94  086 

7-95  5io 
7.96  889 
7.98  225 
7-99  522 

2.05  914 
2.04  490 
2.03  III 

2.01  775 

2.00  478 

9-99  998 
9-99  998 
9-99  998 
9-99  998 
9-99  998 

30 

29 
28 

27 
26 

33i 

37 
38 
39 

8.00  779 
8.  02  002 
8.03  192 
8.04  350 
8.05  478 

1259 
1223 
1190 
1158 
1128 

8.00781 
8.02  004 
8.03  194 
8.04  353 
8.05  481 

1.99  219 
1.97  996 
1.96  806 
1.95  647 

1-94  519 

9-99  998 
9-99  998 
9-99  997 
9-99  997 
9.99  997 

25 
24 
23 

22 
21 

40 

4i 
42 
43 
44 

8.06  578 
8.07  650 
8.08  696 
8.09  718 
8.10717 

1072 
1046 

1022 

999 
976 

954 
934 
914 
896 
877 
860 
843 
827 
812 
797 
782 
769 
755 
743 
73° 

8.06  581 
8.07  653 
8.08  700 
8.09  722 
8.10  720 

1-93  419 
1.92  347 
1.91  300 
1.90  278 
1.89  280 

9-99  997 
9-99  997 
9.99  997 
9.99  997 
9-99  996 

20 

19 
18 

17 
16 

45 
46 

47 
48 
49 

8.  1  1  693 
8.12  647 
8.13  581 
8.14  495 
8.IS  39i 

8.  1  1  696 
8.12  651 

8.13  585 
8.14  500 

8.15  305' 

1.88  304 
1.87  349 
1.86  415 
1.85  500 
1.84  605 

9.99  996 
9-99  996 
9-99  996 
9-99  996 
9.99  996 

15 
14 
13 

12 
II 

50 

Si 
52 
53 
54 

8.16  268 
8.17  128 
8.17  971 
8.18  798 
8.19  610 

8.16  273 

8.17  133 
8.17  976 

8.18  804 
8.19  616 

1.83  727 
1.82  867 
1.82  024 
1.81  196 
x.8o  384 

9-99  995 
9-99  995 
9-99  995 
9-99  995 
9-99  995 

10 

9 
8 

7 
6 

55 
56 
57 
58 
59 

8.20  407 
8.21  189 
8.21  958 

8.22713 
8.23  456 

8.20  413 
8.21  195 
8.21  964 

8.22  720 

8.23  462 

i-79  587 
1-78  805 
1.78  036 
1.77  280 
1.76  538 

9-99994 
9-99  994 
9-99  994 
9-99  994 

9-99  994 

5 
4 
3 

2 

00 

8.24  1  86 

8.24  192 

1.75  808 

9-99  993 

0 

I,.  (  os.      d. 

L.  Cotg. 

C.   d. 

L.Tniic. 

JL.  Sin. 

f 

Prop.  Pts. 

if 

L.  Sin. 

d. 

L.Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

Prop. 

Pts 

o 

I 

2 

3 

4 

8.24  186 
8.24  903 
8.25  609 
8.26  304 
8.26  988 

717 

706 
695 
684 
(,-~ 

8.24  192 
8.24  910 
8.25  616 
8.26  312 
8.26  996 

* 

706 
696 
684 
fit? 

1.75  808 
1.75  090 
1.74  384 
1.73  688 
1.73  004 

9-99  993 
9-99  993 
9-99  993 
9-99  993 
9-99  992 

GO 

II 
11 

5 
6 

7 
8 

9 

8.27  661 
8.28  324 
8.28  977 
8.29  621 
8.30  255 

663 
653 
644 
634 
624. 

8.27  669 
8.28  332 
8.28  986 
8.29  629 
8.30  263 

°73 
663 
654 
643 
634 

62  e 

1.72  331 
1.71  668 
1.71  014 
1.70  371 
1.69  737 

9.99  992 
9.99  992 
9.99  992 
9-99  992 
9.99  991 

55 
54 
53 
52 
5i 

d. 

P.  D.  1" 

d. 

n  TJ  \" 

10 

ii 

12 
13 
14 

8.30  879 

8-31  495 
8.32  103 
8.32  702 
8-33  292 

616 
608 
599 
590 

8.30  888 
8-31  505 

8.32  112 

8.32711 
8.33  302 

6l7 
607 

599 
59i 

-0  . 

1.69  112 

1.68  495 
1.67  888 
1.67  289 
1.66  698 

9-99  991 
9-99  991 
9-99  990 
9.99  990 
9-99  990 

5O 

49 
48 

47 

46 

718 
717 
706 
696 
605 

11.97 

n-95 
11.77 
1  1.  60 
11.58 

485 
480 

475 
474 
470 

8.08 

8.00 

7.92 
7.90 

7  8q 

15 

16 
17 
18 
19 

8-33  875 
8-34  450 
8  35  018 
8-35  578 
8.36  131 

5°3 

575 
568 
560 
553 

8.33  886 
8.34  461 
8-35  029 
8-35  590 
8.36  143 

5°4 

575 
568 
56i 

553 
e/ifi 

1.66  114 

1-65  539 
1.64  971 
1.64  410 
1.63  857 

9-99  99° 
9.99  989 

9-99  989 
9-99  989 
9.99  989 

45 
44 
43 
42 
4i 

684 
673 
663 
654 
653 

11.40 

11.22 
11.05 
10.90 

10.88 

t/v 

464 
460 

459 
455 
450 

7.73 
7.67 
7.65 
7.58 
7.50 

20 

21 
22 
23 
24 

8.36  678 
8.37  217 
8-37  750 
8.38  276 
8.38  796 

539 
533 
526 
520 

8.36  689 
8.37  229 
8.37  762 
8.38  289 
8.38  809 

540 
533 
527 
520 

1.63  311 
1.62  771 
1.62  238 
1.61  711 
1.61  191 

9.99  988 
9-99  988 
9.99  988 
9-99  987 
9-99  987 

40 

39 
38 
37 
36 

644 
643 
634 
625 
624 

10.73 
10.72 

io.57 
10.42 
10.40 

446 

445 
441 

437 
436 

7.43 
7.42 

7.35 

7.28 

7.27 

25 
26 
27 
28 
29 

8.39  3io 
8.39  818 
8.40  320 
8.40  816 
8.41  307 

508 
502 
496 
491 

,0. 

8-39  323 
8.39  832 
8.40  334 
8.40  830 
8.41  321 

509 
502 
496 
491 

A&6 

i.  60  677 
.60  168 
.59  666 
•59  170 
.58  679 

9-99  987 
9.99  986 
9.99  986 
9.99  986 
9-99  985 

35 
34 
33 
32 
3i 

617 
616 
608 
607 
599 

10.28 
10.27 
10.13 

IO.I2 
9.98 

o  8^ 

433 
432 
428 
427 
424 

7.22 

7.20 

7.13 

7.12 

7.07 

30 

3i 
32 
33 
34 

8.41  792 
8.42  272 
8.42  746 
8.43  216 
8.43  680 

480 

474 
470 
464 

8.41  807 
8.42  287 
8.42  762 
8.43  232 
8-43  696 

480 
475 
470 
464 

•58  193 
•57  713 
•57  238 
•56  768 
•56  304 

9.99  985 
9-99  985 
9-99  984 
9-99  984 
9-99  984 

30 

29 
28 
27 
26 

590 
584 
583 
575 
568 

9-83 
9-73 
9.72 

9.58 
9-47 

419 
416 
412 
411 

408 

6.98 

6.93 
6.87 

6.85 

6.80 

35 
36 
37 
38 
39 

8.44  139 
8.44  594 
8.45  044 
8.45  489 
8-45  930 

459 
455 
450 
445 
441 

8.44  156 
8.44  611 
8.45  061 

8-45  507 
8.45  948 

400 

455 
450 
446 
441 

•55  844 
•55  389 
•54  939 
•54  493 
•54  052 

9-99  983 
9-99  983 
9-99  983 
9-99  982 
9.99  982 

25 
24 

23 

22 

21 

56i 
560 

553 
547 
546 

9-35 
9-33 
9.22 
9.12 
9.10 

404 
401 
400 
397 
396 

6.73 
6.68 
6.67 
6.62 
6.60 

4O 

4i 
42 
43 
44 

8.46  366 
8.46  799 
8.47  226 
8.47  650 
8.48  069 

43° 

433 
427 
424 
419 
A,f. 

8.46  385 
8.46  817 
8-47  245 
8.47  669 
8.48  089 

437 

432 
428 

424 
420 

Atft 

•53  615 
•53  183 
1-52  755 
•52  33i 
.51  911 

9-99  982 
9-99  981 
9.99  981 
9-99  98i 
9-99  98o 

20 

19 

18 

17 
16 

540. 
539 
533 

527 
526 

9.00 
8.98 
8.88 
8.78 

8-77 

393 
39° 
386 

383 
382 

£'55 
6.50 

6-43 
6.38 
6-37 

45 
46 

47 
48 
49 

8.48  485 
8.48  896 
8.49  304 
8.49  708 
8.50  108 

411 

408 
404 
400 

qo6 

8.48  505 
8.48  917 

8-49  325 
8.49  729 
8.50  130 

412 

408 
404 
401 

•5i  495 
•Si  083 
•50  675 
.50  271 
.49  870 

9.99  980 
9-99  979 
9-99  979 
9-99  979 
9-99  978 

15 
14 
13 

T2 
II 

520 
514 
5<>9 
508 
502 

4O6 

O.O7 

8-57 
8.48 

8.47 
8.37 
8.27 

380 

379 
376 
373 
370 
q6o 

6-33 
6.32 
6.27 

6.22 

6.17 

6  15 

5O 

Si 
52 
53 
54 

8.50  504 
8.50  897 
8.51  287 
8-51  673 
8.52  055 

393 
39° 
386 
382 

8.50  527 
8.50  920 
8.51  310 
8.51  696 
8.52  079 

393 
390 
386 
383 

•49  473 
.49  080 
.48  690 
.48  304 
•47  921 

9-99  978 
9-99  977 
9.99  977 
9.99  977 
9.99  976 

10 

9 
8 

7 
6 

491 
486 

8.18 
8.10 

* 

367 

363 

6.12 

6.05 

55 
56 
57 
58 
59 

8.52  434 
8.52  810 
8-53  183 
8-53  552 
8-53  919 

379 
376 
373 
369 
367 
•36-3 

8.52  459 
8.52  835 
8.53  208 
8-53  578 
8-53  945 

3°° 
376 
373 
37° 
367 
•afii 

•47  541 
•47  165 
.46  792 
.46  422 
•46  055 

9-99  976 
9-99  975 
9-99  975 
9-99  974 
9-99  974 

5 
4 
3 

2 

I 

6O 

8.54  282 

8.54  308 

1.45  692 

9-99  974 

O 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.Tang. 

L.  Sin. 

/• 

Prop. 

Pts, 

88< 


/• 

I..  Sin. 

d. 

L.Taiig. 

c.  d. 

L.  Cotg. 

L.  Cos. 

Prop.  Pts. 

o 

I 

2 

3 
4 

8.54  282 
8.54  642 
8.54  999 
8-55  354 
8.55  705 

360 

357 
355 
35i 
349 
346 
343 
34i 
337 
336 
332 
33<> 
328 
325 
323 
320 
3i8 
316 
313 
3" 
3°9 
307 
3°5 
302 
301 
298 
296 
294 

293 
290 

288 
287 
284 
283 
281  ' 

8.54  308 
8.54  669 
8-55  027 
8.55  382 
8-55  734 

361 

358 

355 
352 
349 
346' 
344 
34i 
338 
336 
333 
33° 
328 
326 
323 
321 
3i9 
316 
314 
3" 
310 
3°7 
3<>5 
303 
301 
299 
297 
295 
292 
291 
289 
287 
285 
284 
28-1 
280 
278 
276 
274 
273 
271 
269 
268 
266 
.264 
263 
261 
260 
258 
257 

255 
254 
252 
251 
249 
248 
246 
245 
244 
*43 

1.45  692 
i-45  33i 
1-44  973 
1.44  618 
1.44  266 

9  99  974 
9-99  973 
9-99  973 
9.99  972 
9.99  972 

6O 

59 
58 
57 
56 

P-P-1' 
6.  02 
6.00 
5-97 
5-95 
5-92 
5.87 
5.85 
5-82 
5-77 
5-73 
5-72 
5-68 
5-63 
^.62 
5-6o 
5-55 
5-53 
5-5° 
5*47 
5-43 
5-42 
5-38 
5-35 
5.33 
5-32 
5-3° 
5-27 
5-23 
5.22 
5-i8 
5.17 
5-15 

5-12 

5-08 
5-05 
5.03 
5.02 
4.98 
4-97 
4-95 
4-93 
4.92 
4.90 
4.88 
4-87 

d. 

291 
290 
289 
288 
287 
285 
284 
283 
281 
280 

279 
278 

277 
276 

274 
273 
272 
271 
270 
269 
268 
267 
266 
264 
263 
261 
260 
259 
258 
257 
256 

255 
254 
253 
252 

251 
250 

249 
248 
247 
246 
245 
244 
243 
242 

p.p.l" 

4-85 
4-83 
4.82 
4.80 
4.78 
4-75 
4-73 
4.72 
4.68 
4.67 
4.65 
4-63 
4.62 
4.60 
4-57 
4-55 
4-53 
4-52 
4-50 
4.48 
4-47 
4-45 
4-43 
4.40 

4.38 
4-35 
4-33 
i32 
4-30 
4.28 
4.27 
4-25 
4-23 
4.22 
4.20 
4.18 
4.17 
4-15 
4-13 
4-1? 
4.10 
4.08 
4.07 
4-05 
4-03 

1 

7 
8 

9 

8.56  054 
8.56  400 
8.56  743 
8-57  084 
8.57  421 

8.56  083 
8.56  429 
8-56  773 
8.57  114 
8-57  452 

1-43  917 
1-43  57i 
1-43  227 
1.42  886 
1.42  548 

9-99  971 
9.99  971 
9-99  970 
9.99  970 

9-99  969 

55 
54 
53 
52 
5i 

d. 

1O 

ii 

12 
13 
14 

8-57  757 
8.58  089 
8.58  419 
8.58  747 
8.59  072 

8.57  788 

8.58   121 
8-58  451 

8.58  779 
8-59  105 

1.42  212 

1.41  879 

1.41  549 

I.4I  221 
1.40  895 

9-99  969 
9-99  968 
9-99  968 
9-99  967 
9.99  967 

5O 

49 

48 

47 
46 

361 
360 
358 
357 
355 
352 
35i 
349 
346 
344 
343 
34i 
338 
337 
336 
333 
332 
33° 
328 
326 
325 
323 
321 
320 
319 
3i8 
316 
3*4 
3i3 
3" 
310 
3°9 
307 
3°5 
303 
302 
301 
299 
298 
297 
296 
295 
294 
293 
292 

15 

16 

17 
18 

19 

8-59  395 
8-59  715 
8.60  033 
8.60  349 
8.60  662 

8.59  428 

8-59  749 
8.60  068 
8.60  384 
8.60  698 

1.40  572 
1.40  251 

1-39  932 
1.39  616 
1-39  3°2 

9-99  967 
9.99  966 
9.99  966 

9-99  965 
9.99  964 

45 
44 
43 
42 
41 

20 

21 
22 
23 
24 

8.60  973 
8.61  282 
8.61  589 
8.61  894 
8.62  196 

8.61  009 
8.61  319 
8.61  626 
8.61  931 
8.62  234 

1.38  991 
1.38  681 
1-38  374 
1.38  069 
1.37  766 

9.99  964 
9-99  963 
9-99  963 
9-99  962 
9-99  962 

40 

39 
38 
37 
36 

25 
26 
27 
28 
29 

8.62.497 
8.62  795 
8.63  091 
8.63  385 
8.63  678 

8.62  535 
8.62  834 
8.63  131 
8.63  426 
8.63  718 

*-37  465 
1.37  166 
1.36  869 

1-3.6  574 
1.36  282 

9-99  96i 
9-99  961 
9-99  96o 
9-99  960 
9-99  959 

35 
34 
33 
32 
3i 

30 

3i 
32 

33 
34 

8.63  968 
8.64  256* 

8-64  543 
8.64  827 
8.65  no 

8.64  009 
8.64  298 
8.64  585 
8.64  870 
8.65  154 

i-35  99i 
1.35  70^ 

1.35  415 
1-35  130 
1.34  846 

9-99  959 
9-99  958 
9-99  958 
9-99  957 
9-99  956 

30 

29 
28 
27 
26 

35 
36 
37 
38 
39 

8.65  391 
8.65  670 
8.65  947 
8.66  223 
8.66  497 

'279 
277 
276 
274 
272 
270 
269 
267 
266 
263 
263 
260 

259 
258 

8-65  435 
8-65  715 
8-65  993 
8.66  269 
8.66  543 

i-34  565 
i-34  285 
1.34  007 
1-33  73i 
1-33  457 

9-99  956 
9-99  955 
9-99  955 
9-99  954 
9-99  954 

25 
24 

23 

22 
21 

40 

4i. 
42 
43 
44 

8.66  769 
8.67  039 
8.67  308 
8.67  575 
8.67  841 

8.66  816 
8.67  087 
8.67  35-6 
8.  "67  624 
8.67  890 

1-33  184 
1.32  913 
1.32  644 
1.32  376 
1.32*110 

9-99  953 
9-99  952 
9-99  952 
9-99  951 
9-99  95  ! 

20 

19 

18 

17 
16 

45 
46 
47 
48 
49 

8.68  104 
8.68  367 
8.68  627 
8.68  886 
8.69  144 

8.68  154 
8.68  417 
8.68  678 
8.68  938 
8.69  196 

1.31  846 

1-31  583 
1.31  322 
1.31  062 
1.30  804 

9-99  950 
9-99  949 
9.99  949 
9-99  948  . 
9-99  948 

15 

14 
13 

12 
II 

50 

Si 
52 
53 
54 

8.69  400 
8.69  654 
8.69  907 
8.70  159 
8.70  409 

250 
254 
253 
252 
250 

8-69  453 
8.69  708 
8.69  962 
8.70  214 
8.70  46? 

1-30  547 
1.30  292 
1.30  038 
1.29.786 
1-29  535 

9-99  947 
9.99  946 

9-99  946 
9-99  945 
9-99  944 

10 

9 
8 
7 
6 

55 
56 
57 
58 
59 

8.70  658 
8.70  90? 
8.71  151 

8-71  395 
8.71  638 

249 
247 
246 
244 
243 

8.70  714 
8.70  962 
8.71  208 

8-71  453 
8.71  697 

1.29  286 
1.29  038 
1.28  792 
1.28  547 
1.28  303 

9-99944 
9-99  943 
9-99  942 
9.99  942 
9.99  941 

5 

4 
3 

2 

I 

0 

GO 

8.71  880 

243 

8.71  940 

1.28  060 

9-99  940 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.Taiif;. 

L.  Sin. 

/ 

Prop.  Pts. 

87< 


r 

L,.  Siu. 

d. 

L.Tang.jc.  d.|  L.  Cotg. 

L.  Cos. 

Prop. 

Pts. 

0 

i 

2 

3 

4 

8.71  880 

8.72  120 

8.72  359 
8.72  597 
8.72  834 

240 

239 
238 

237 
235 

234 
232 
232 
230 
229 
228 
226 
226 
224 
223 

222 
220 

220 
2I9 
2I7 

216 
216 

2I4 
2I3 
212 
2X1 
210 
209 
208 
208 
206 
205 
204 
203 
2O2 
2OI 
201 
I99 
199 
197 
197 
I96 
195 
I94 

life 
I92 
192 
I90 
190 
189 

188 
187 

187 
1  86 
185 
184 
183 
183 
181 
181 

8.71  940 
8.72  181 
8.72  420 
8.72  659 
8.72  896 

241 

239 
239 

237 
236 

234 
234 
232 
231 
229 
229 
227 
226 
225 
224 

222 
222 
220 
2I9 
2I9 
2I7 
2l6 

215 
214 
213 

211 
211  < 

210 
209 
208 
206 
206 
205 
204 

2*3 

202 
2O  I 
201 
I99 
I98 
I98 
I96 
I96 

'95 
194 

193 
192 
192 
190 
190 
189 
188 
188 
186 
186 

185 
184 
184 
182 
182 

1.28  060 
1.27  819 
1.27  580 
1.27  341 
1.27  104 

9-99  940 
9.99  940 

9-99  939 
9-99  938 
9-99  938 

60 

59 
58 

1 

6 

7 
8 

9 

10 
20 
30 
40 
50 

6 

7 
8 

9 

10 
20 

30 
40 

50 

6 
7 
8 
9 

10 
20 
30 
40 
50 

6 

7 
8 

9 

10 
20 

30 
40 

50 

6 

7 
8 

9 

10 

20 

3° 
4° 
50 

6 

7 
8 

"9 

10 
20 

30 
40 

50 

438 

23.8 
27-8 
31-7 
35-7 
39-7 
79-3 
119.0 

158.7 
198-3 
225 
22.5 
26.3 
30.0 
33-8 
37-5 
75-0 
112.5 
150.0 
187.5 

212 

"21.2 
24.7 
28.3 
3L8 
35-3 
70.7 

106.0 

141-3 
176.7 

2OI 
20.1 

23-5 
26.8 
30.2 

33-5 
67.0 
100.5 
134.0 
167.5 
189 
18.9 

22.1 
25.2 
28.4 

SI'S 
63.0 

94-5 
126.0 

157.5 

4 

6.4    c 
0.5    c 
0.5    c 
0.6    c 
0.7    c 
i-3    i 

2.0     J 

2.7    i 

3-3    '- 

234 

23-4 
27-3 
31.2 
35-1 
39-o 
78.0 
117.0 
156.0 
195-0 

220 
22.0 

25-7 
29-3 

33-o 
36.7 
73-3. 

IIO.O 

146.7 
183-3 
208 

20.8 

24-3 
27.7 
31.2 

34-7 
69-3 
104.0 

138.7 
173-3 
197 
19.7 
23.0 
26.3 
29.6 
32.8 
65-7- 
98.5 
I3L3 
164.2 

185 
18.5 

21.6 

24.7 
27.8 

30.8 
61.7 
92.5 
123-3 
1542 

3       « 

)-3     0.2 
)-4     0.2 

>-4    0.3 
>-5    0.3 
>-5    0.3 
.0    0.7 
•5    1.0 
..o    1.3 

'•5    i-7 

229 

22.9 
26.7 
30.5 

34-4 
38.2 

76.3 
"4-5 
152.7 
190.8 

216 

21.6 

25.2 
28.8 
32.4 
t  36.0 
72.0 

108.0 

144.0 

180.0 

204 

20.4 

23.8 

27.2 

30.6 

34-0 
68.0 

102.0 
136.0 
170.0 

193 

19-3 
22-5 
25.7 
29.0 
32.2 
6J.3 
96.5 
128.7 
160.8 

181 
18.1 

21.  1 
24.1 
27.2 
30.2 
60.3 

9°-5 
120.7 
150.8 

z 

O.I 
O.I 
O.I 
0.2 
O.2 
0-3 

0.5 

0.7 

0.8 

6 
7 
8 

9 

8.73  069 
8-73  303 
8-73  535 
8-73  767 
8-73  997 

8.73  132 
8.73  366 
8.73  600 
8.73  832 
8.74  063 

1.26  868 
1.26  634 
1.26  400 
1.26.168 
1.25  937 

9-99  937 
9.99  936 

9-99  936 
9-99  935 
9-99  934 

55 
54 
53 
52 
5i 

10 

ii 

12 
13 

14 

8.74  226 

8-74  454 
8.74  680 
8.74  906 
8-75  130 

8.74  292 
8.74  52i 
8.74  748 
8.74  974 
8-75  199 

1.25  708 

1.25  479 
1.25  252 
1.25  026 
1.24  801 

9-99  934 
9-99  933 
9.99  932 
9.99  932 
9-99  931 

50 

49 
48 
47 
46 

15 

16 

17 
18 

19 

8-75  353 
8-75  575 
8-75  795 
8.76  015 
8.76  234 

8-75  423 
8-75  645 
8.75  867 
8.76  087 
8.76306 

1-24  577 
1-24  355 

1-24  133 
1.23  913 
1.23  694 

9-99  930 
9.99  929 
9.99  929 
9-99  928 
9-99  927 

45 
44 
43 
42 

4i, 

20 

21 
22 
23 
24 

8.76  451 
8.76  667 
8.76  883 

8-77  097 
8.77  310 

8.76  525 
8.76  742 
8.76  958 
8.77  173 
8.77  387 

1.23  475 
1.23  258 
1.23  042 

'  1.22  827 
1.22  613 

9.99  926 
9-99  926 
9-99  925 
9.99  924 
9.99  923 

40 

39 
38 

% 

25 
26 
27 
28 
29 

8.77  522 
8.77  733 
8-77  943 
8.78  152 
8.78  360 

8.77  600 
8.77  811 

8.78  022 
8.78  232 
8.78  441 

1.22  400 
1.22  189 
"  I.2I  978 
I.2I  768 

i.2i  559 

9-99  923 
9  99  922 
9.99  921 
9.99  920 
9.99  920 

35 
34 
33 
32 
3i 

30 

31 
32 
33 
34 

8.78  568 
8.78  774 
8.78  979 
8.79  183 
8.79  386 

•    8.78  649 
8.78  855 

8.79  061 
8.79  266 
8.79  470 

1.  21  351 
'   I.2I   145 

1.20  939 
1.20  734 
1.20  530 

9-99  919 
9-99  9i8 
9.99  917 

9-99  917 
9.99  916 

3O 

29 
28 
27 
26 

It 

37 
38 
39 

8.79  588 
8-79  789 
8-79  990 
8.80  189 
8.80  388 

8.79  673 

8-79  875 
8.80  076 
8.80  277 
8.80  476 

1.20  327 
1.20  I2g 
I.I9  924 
I.I9  723 
I.I9.524 

9-99  9*5 
9-99  914 
9-99  913 
9-99  9*3 
9-99  912 

25 
24 
23 

22 
21 

40 

4i 
42 
43 
44 

8.80  585 
8.80  782 
8.80  978 
8.81  173 
8.81  367 

8.80  674 
8.80  872 
8.81  c68 
8.81  264 
8.81  459 

I.I9  326 
I.I9  128 

1.18  932 
1.18  736 
1.18  541 

9.99  911 
9-99  9io 
9-99  909 
9.99  909 

9-99  9°8 

20k 

19 
18 

17 
16 

45 
46 

47 
48 
49 

8.81  560 
8.81  752 
8.81  944 
8.82  134 
8.82  324 

8.81  653 
8.8l  846 
8.82  038 
8.82  230 
8.82  420 

1.18  347 
1.18  154 
1.17  962 
1.17  770 
1.17  580 

9-99  9°7 
9-99  9°6 
9  99  9°5 
9-99  904 
9.99904 

15 
H 
13 

12 
II 

50 

5i 

52 
53 
54 

8.82513 
8.82  701 
8.82  888 
8.83  075 
8.83  261 

8.82  610 
8.82  799 
8.82  987 
8-83  175 
8.83  361 

1.17  390 

I.I7  201 
I.I7  OI3 

1.16  825 
1.16  639 

9.99  903 
9.99  902 
9-99  90i 
9-99  900 
9-99  ^99 

10 

9 
8 

7 
6 

55 
56 
57 
58 
59 

8.83  446 
8.83  630 
8.83  813 
8.83  996 
8.84  177 

8.83  547 
8.83  732 
8.83  916 
8.84  100 
8.84  282 

1-16  453 
1.16  268 
1.16  084 
1.15900 
1.15  718 

9.99  898 
9-99  898 
9-99  897 
9-99  896 
9.99  895 

5 
4 
3 

2 

I 

60 

8.84  358 

8.84  464 

I.I5  536 

9-99  894 

0 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.Tang. 

L.  Sin. 

/• 

Prop.  Pts. 

86C 


26 


/• 

L.  Sin. 

d. 

L.Tang. 

c.  d. 

L.  Cotg. 

T,.  Cos. 

Pro 

p.  Ft;- 

o 

I 

2 

3 

4 

8.84  358 
8-84  539 
8.84  718 
8.84  897 
8.85  075 

181 

179 
179 

178 

8.84  464 
8.84  646 
8.84  826 
8.85  006 
8.85  185 

182 
180 
180 
179 

1-15  536 
I-I5  354 
I.I5  174 
1.14  994 
1.14815 

9.99  894 
9.99  893 
9-99  892 
9-99  891 
9-99  891 

60 

59 
58 
57 
56 

6 
7 
8 

1  80 
18.0 

2I.O 
24.0 

177 
17.7 
20.7 
23-6 

174 
17.4 
20.3 
23.2 

5 
6 

7 
8 
9 

8.85  252 
8.85  429 
8.85  605 
8.85  780 
8-85  955 

177 
177 
176 
i75 
*75 

8.85  363 
8.85  540 

8-85.717 
8.85  893 
8.86  069 

178 
177 
177 
176 
176 

1.14  637 
1.14  460 
1.14  283 
1.14  107 
I-I3  93i 

9-99  890 
9-99  889 
9.99  888 
9-99  887 
9.99  886 

55 
54 
53 
52 
Si 

9 

10 

20 
30 
40 

27.0 
30.0 
6o.O 
90.0 
I2O.O 

26.6 
29-5 
59-° 
88.5 
118.0 

26.1 
29.0 
58.0 
87.0 
116.0 

10 

ii 

12 
13 
14 

8.86  128 
8.86  301 
8.86  474 
8.86  645 
8.86  816 

173 
173 
173 
171 
171 

8.86  243 
8.86  417 
8.86  591 
8.86  763 
8.86  935 

*74 
174 
174 
172 
172 

1.13  757 
I.I3  583 
1.13  409 
1.13  237 
1.13  065 

9-99  885 
9-99  884 
9-99  883 
9.99  882 
9.99  881 

5O 

49 
48 
47 
46 

5° 

6 

7 
8 

171 
I7.I 
20.0 
22.8 

X47-S 
169 
16.9 
19.7 
22.5 

I45-° 
167 
16.7 
19-5 
22.3 

15 

16 
17 
18 
19 

8.86  987 
8.87  156 
8.87  325 
8.87  494 
8.87  661 

171 
169 
169 
169 
167 

ififi 

8.87  106 
8.87  277 
8.87  447 
8.87  616 
8.87  785 

171 
171 
170 
J69 
169 

1.  12  894 
1.  12  723 

i.i2  553 
1.  12  384 

1.  12  215 

9.99  880 
9-99  879 
9-99  879 
9.99  878 
9.99  877 

45 
44 
43 
42 
4i 

9 

10 

20 

30 
40 

25-7 
28.5 

57-0 
85-5 
114.0 

25-4 
28.2 

56.3 
84.5 
112.7 

T  in  R 

25.1 

27.8 
55-7 
83-5 
111.3 

20 

21 
22 

23 
24 

8.87  829 
8.87  995 
8.88  161 
8.88  326 
8.88  490 

166 
166 
165 
164 

8.87  953 
8.88  120 
8.88  287 
8.88  453 
8.88  618 

167 
167 
166 
165 

1.  12  047 
I.  II  880 
I.  II  713 

i.  ii  547 
i.  n  382 

9.99  876 

9-99  875 
9.99  874 

9-99  873 
9.99  872 

40 

39 
38 
37 
36 

5° 

6 

7 
8 

142.5 
165 
16.5 
19-3 

22.0 

140.8 
I63 

I6.3 
19.0 
21.7 

139.2 
1  60 
16.0 
18.7 
21.3 

25 
26 
27 
28 
29 

8  88  654 
8.88  817 
8.88  980 
8.89  142 
8.89  304 

163 
163 
162 
162 
160 

8.88  783 
8.88  948 
8.89  in 
8.89  274 
8.89  437 

105 

165 
163 
163 
163 
161 

i.  n  217 
i.  n  052 

I.  10  889 

i.  10  726 
i.io  563 

9-99  871 
9-99  870 
9  99  869 
9.99  868 
9-99  867 

35 
34 
33 
32 
3i 

9 

10 

20 

3° 
40 

24.8 
27-5 

55-0 
82.5 

IIO.O 

24-5 

27.2 

54-3 
81.5 
108.7 

24.0 
26.7 

53-3 
80.0 
106.7 

30 

3i 
32 
33 
34 

8.89  464 
8.89  625 
8.89  784 
8.89  943 

8.90  102 

161 

159 
159 
J59 

8.89  598 
8.89  760 
8.89  920 
8.90  080 
8.90  240 

162 
160 
160 
160 

i.io  402 
i.io  240 
i.io  080 
1.09  920 
1.09  760 

9.99  866 
9-99  865 
9-99  864 
9-99  863 
9.99  862 

30 

29 
28 

27 
26 

-5° 

6 

7 
8 

J37-5 
i57 
iS-7 
18.3 
20.9 

I35-° 
155 

15-5 
18.1 
20.7 

J33-3 
153 

15-3 
17.9 
20.4 

35 
36 
37 
38 
39 

8.90  260 
8.90  417 

8.90  574 
8.90  730 
8.90  885 

158 

157 
»57 

156 
155 

8.90  399 
8.90  557 
8.90  715 
8.90  872 
8.91  029 

T59 

158 
158 
157 
157 

tcfi 

1.09  60  1 
1.09  443 
1.09  285 
1.09  128 
i.  08  971 

9  99  861 
9.99  860 
9-99  859 
9-99  858 
9-99  857 

25 
24 
23 

22 

21 

9 

10 
20 

30 
40 

23.6 
26.2 
52.3 
78.5 
104.7 

23-3 
25-8 
51-7 
77-5 
103-3 

23.0 

25-5 
51.0 

76.5 

102.0 

40 

4i 
42 
43 
44 

8.91  040 
8.91  195 
8.91  349 
8.91  502 
8-91  655 

!55 
»55 
*54 
153 

»53 

8.91  185 
8.91  340 
8.91  495 
8.91  650 
8.91  803 

155 
155 
155 
153 

1.08  815 
i.  08  660 
i.  08  505 
i.  08  350 
1.08  197 

9-99  856 
9-99  855 
9-99  854 
9-99  853 
9-99  852 

20 

19 

18 

17 
16 

b° 

6 

7 
8 

130.0 
151 

I5A 
I7.6 

20.1 

149 
14.9 

17-4 
19.9 

I27-5 

147 
14.7 
17.2 
19.6 

45 
46 

47 
48 
49 

8.91  807 
8.91  959 
8.92  no 
8.92  261 
8.92  411 

152 
152 
151 
151 
150 

8.91  957 
8.92  no 
8.92  262 
8.92  414 
8.92  565 

X54 
153 
i52 
152 
*5i 

i.  08  043 
1.07  890 
1.07  738 
1.07  586 
1-07  435 

9-99  851 
9  99  850 
9-99  848 
9-99  847 
9.99  846 

15 
14 
13 

12 

II 

9 
10 

20 
30 
40 

22.7 
25-2 
50-3 

75-5 
100.7 

22.4 
24.8 
49-7 
74-5 
99-3 

22.1 

24-5 
49.0 

73-5 
98.0 

50 

Si 
52 
53 
54 

8.92  561 
8.92  710 
8.92  859 
893007 
8-93  154 

150 

*49 

1  49 
148 
M7 

8.92  716 
8.92  866 
8.93  016 
8-93  I65~ 
8.93  313 

X5X 
150 
150 
149 
148 

1.07  284 
1.07  134 
i.  06  984 
1.06  835 
i.  06  687 

9-99  845 
9-99  844 
9-99  843 
9.99  842 

9-99  841 

10 

9 
8 
7 
6 

i>° 

146 
6      14- 
7      17- 
8      19- 

a 

6     0.2 
0     0.2 

5    0.3 

122.5 

i 

O.I 
O.I 
O.I 

55 
56 
57 
58 
59 

8.93  3oi 
8.93  448 

8-93  594 
8.93  740 
8.93  885 

'47 

'47 
146 
146 
MS 

8.93  462 
8.93  609 
8-93  756 
8  93  903 
8.94  049 

J49 
»47 
»47 
»47 
146 

1.06  538 
1.06  391 
i.  06  244 
i.  06  097 
1-05  951 

9-99  840 
9-99  839 
9.99  838 

9-99  837 
9-99  836 

5 
4 
3 

2 
I 

i 

2 

3 
4 

9      21. 
o      24. 
o     48. 

o      73- 
o     97. 

9    o-3 
3    °-3 
7    0.7 

0     I.O 

3    1-3 

0.2 
0.2 

0-3 
0-5 
0.7 

60 

8.94  030 

145 

8.94  195 

140 

1.05  805 

9-99  834 

0 

b 

O     121. 

7    1-7 

o.o 

L.  Cos. 

(I. 

i  .  rotg. 

C.    (1. 

L.TniiK. 

L.  Sin. 

/ 

Fro] 

).    PIS 

85C 


r 

L.  Sin. 

d. 

L.Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

Pro] 

>.   PtH 

• 

O 

i 

2 

3 

4 

8.94  030 
8.94  174 
8.94  317 
8.94  461 
8.94  603 

144 
143 
i44 
142 

8.94  195 
8.94  340 
8.94  485 
8.94  630 
8-94  773 

145 
145 
145 
143 

1.05  805 
1.05  660 

1.05  5i5 
1.05  370 
1.05  227 

9-99  834 
9-99  833 
9-99  832 
9.99  831 
9-99  830 

6O 

59 
58 

| 

6 

7 
8 

MS 

14-5 
16.9 

19-3 

'43 

14-3 
I6.7 
I9.I 

141 

I4-I 
16.5 

18.8 

5 
6 

7 
8 

9 

8.94  746 
8.94  887 
8.95  029 
8.95  170 
8-95  3io 

141 
142 
141 
140 

8.94  917 
8.95  060 

8.95  202 

8-95  344 
8.95  486 

143 
142 
142 
142 

1.05  083 
1.04  940 
1.04  798 
1.04  656 
1.04  514 

9-99  829 
9.99  828 
9.99  827 
9-99  825 
9-99  824 

55 
54 
53 
52 
5i 

9 

10 
20 

30 
40 

21.8 

24.2 
48.3 
72.5 
96.7 

I2O  8 

21-5 

23-8 

47-7 
71.5 
95-3 

21.2 
23-5 

47.0 

70.5 
94.0 

117  ^ 

10 

ii 

12 

13 
14 

8-95  450 
8-95  589 
8.95  728 
8-95  867 
8.96  005 

139 
139 
139 
138 
j-,0 

8.95  627 

8-95  767 
8.95  908 
8.96  047 
8.96  187 

140 
141 

139 
140 

Tl8 

1-04  373 
1.04  233 
1.04  092 

1-03  953 
1.03  813 

9-99  823 
9.99  822 
9.99  821 
9.99  820 
9-99  819 

50 

49 
48 

47 
46 

6 
7 
8 

139 
13.9 

16.2 

18.5 

138 
13-8 
16.1 

18.4 

I36 
13-6 
15-9 

18.1 

15 

16 

17 
18 

19 

8.96  143 
8.96  280 
8.96  417 

8.96  553 
8.96  689 

137 
137 
136 
136 
176 

8.96  325 
8  96  464 
8.96  602 
8.96  739 
8.96  877 

I3° 
139 
138 
137 
138 
lift 

1.03  675 
1.03  536 
1.03  398 
1.03  261 
1.03  123 

9-99  817 
9.99  816 

9-99  815 
9-99  814 
9  99  813 

45 
44 
43 
42 

4i 

9 

10 
20 
30 
40 

20.9 

23.2 

46.3 

69.5 

92.7 

TTC  8 

20.7 
23.0 
46.0 
69.0 
92.0 

20.4 
22.7 

45-3 
68.0 
90.7 

2O 

21 
22 

23 

24 

8.96  825 
8.96  960 
8-97  095 
8.97  229 
8-97  363 

135 

J35 
134 
J34 

8.97  013 
8.97  150 
8.97  285 
8.97  421 
8-97  556 

137 
135 
136 
135 

1.02  987 
1.02  850 
1.02  715 

1.02  579 

1.02444 

9.99  812 
9.99  810 
9.99  809 
9.99  808 
9.99  807 

40 

39 

38 

P 

5° 

6 

7 
8 

135 
13-5 
15.8 

18.0 

133 
13-3 

15-5 
17.7 

iAO  J 

131 
I3-I 

15-3 
17.5 

25 
26 

27 
28 
29 

8.97  496 
8.97  629 
8.97  762 
8.97  894 
8.98  026 

133 
133 
132 
132 

8.97  691 
8.97  825 

8-97  959 
8.98  092 
8.98  225 

134 
134 
133 
133 

1.02  309 
1.02  175 
1.02  041 

i.oi  908 
i.  oi  775 

9.99  806 
9-99  804 
9.99  803 
9.99  802 
9.99  801 

35 
34 
33 
32 
3i 

9 

10 
20 

30 
40 

20.3 

22.5 
45-0 
67.5 
90.0 

20.0 
22.2 

44-3 
66.5 
88.7 

19.7 

21.8 

43-7 
65.5 
87.3 

30 

3i 
32 
33 
34 

.8.98  157 
8.98  288 
8.98  419 
8.98  549 
8.98  679 

131 
131 
130 
130 

8.98  358 
8.98  490 
8.98  622 
8.98  753 
8.98  884 

J33 
132 
132 
»3i 
131 

i.oi  642 
i.oi  510 
i.oi  378 
i.oi  247 
i.oi  116 

9.99  800 
9.99  798 
9-99  797 
9-99  796 
9-99  795 

30 

29 

28 

27 
26 

Su 

6 

7 

8 

112.5 
129 
12.9 

iS-i 
17.2 

128 

12.8 

14.9 
17.1 

126 

12.6 

14.7 

16.8 

H 

37 
38 
39 

8.98  808 
8.98  937 
8.99  066 
8.99  194 
8.99  322 

129 
129 
128 
128 
128 

8.99  015 
8-99  145 
8.99  275 
8.99  405 
8-99  534 

I31 
130 
130 
130 
129 
128 

i.oo  985 
i.oo  855 
i.oo  725 
i.oo  595 

I.OO  466 

9-99  793 
9.99  792 
9.99  791 
9-99  790 
9-99  788 

25 
24 

23 

22 
21 

9 

10 
20 
30 
40 

19.4 
21.5 
43-o 
64.5 
86.0 

19.2 

21.3 

42.7 

64.0 

85.3 

18.9 

21.0 

42.0 
63.0 
84.0 

40 

41 

42 

43 
44 

8-99  450 
8-99  577 
8-99  704 
8.99  830 
8-99  956 

127 

127 
126 
126 
126 

8.99  662 

8-99  79i 
8.99  919 
9.00  046 
9.00  174 

129 
128 
127 
128 

i.oo  338 
i.oo  209 
i.oo  081 

0.99  954 
0.99  826 

9-99  787 
9.99  786 

9-99  785 
9-99  783 
9-99  782 

20 

19 
18 

17 
16 

50 

6 

7 
8 

i°7-5 
«5 
12.5 
14.6 
16.7 

123 
12.3 
14.4 

16.4 

122 
12.2 
14.2 
I6.3 

45 
46 
47 
48 
49 

9.00  082 
9.00  207 
9.00  332 
9.00  456 
9.00  581 

125 
125 
124 
125 

9.00  301 
9.00  427 

9-00  553 
9.00  679 
9.00  805 

126 
126 
126 
126 

0.99  699 
o-99  573 
o.99  447 
0.99  321 
0.99  195 

9-99  78i 
9.99  780 
9.99  778 
9-99  777 
9-99  776 

IS 
14 
13 

12 

II 

9 

10 
20 

3° 

40 

18.8 

20.8 

41.7 
62.5 
83-3 

18.5 

20.5 
41.0 

61.5 

82.0 

I8.3 
20.3 
40.7 

61.0 
81.3 

5O 

5i 

52 
53 
54 

9.00  704 
9.00  828 
9.00  951 
9.01  074 
9.01  196 

124 
123 
123 

122 

9.00  930 
9.01  055 
9.01  179 
9.01  303 
9.01  427 

125 
124 
124 
124 

0.99  070 
0.98  945 
0.98  821 
0.98  697 
0.98  573 

9-99  775 
9-99  773 
9-99  772 
9-99  771 
9-99  769 

10 

9 
8 

7 

6 

50 

e 

121 
i        I2.I 
r       14.1 
5      16.1 

I2O 
I2.C 
I4.C 

i6.c 

z 

O.I 
O.I 
O.I 

55 
56 
57 
58 
59 

9.01  318 
9.01  440 
9.01  561 
9.01  682 
9.01  803 

122 
121 
121 
121 

9.01  550 
9.01  673 
9.01  796 
9.01  918 
9.02  040 

123 
123 
123 

122 
122 

0.98  450 
0.98  327 
0.98  204 
0.98  082 
o  97  960 

9.99  768 
9-99  767 
9-99  765 
9-99  764 
9-99  763 

5 
4 

3 

2 

I 

c 

1C 
2C 

3< 
4< 

)      18.2 

)        2O.2 

>        40-3 
)        60.5 
)        80.7 

i8.c 

2O.C 

40.c 
6o.c 
8o.c 

0.2 
O.2 
»     0.3 
>     0.5 

>     0.7 

6O 

9.01  923 

9.02  162 

0.97  838 

9.99  761 

O 

b< 

)    100.8 

IOO.C 

>    0.8 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.Tang. 

L.  Sin. 

/• 

Pro] 

p.   PtB 

84( 


6° 


/• 

L.  Sin. 

d. 

L.Taug. 

c.  d. 

L.  Cotg. 

L.  Cos. 

Prop.  Pts. 

o 

I 

2 

3 

4 

9.01  923 
9.02  043 
9.02  163 
9.02  283 
9.02  402 

20 
20 
20 

19 
18 

'9 

18 
117 
118 
117 
117 
116 
xx6 
116 
116 

"5 
"5 
114 
"5 
"3 
114 
114 
"3 

113 

"3 

112 
112 
112 
III 
III 
III 
110 
110 
110 

no 

109 
109 
109 

108 
109 
1  08 
107 
1  08 
107 
107 
106 
107 
1  06 
105 
106 

9.02  162 
9.02  283 
9.02  404 
9.02  525 
9.02  645 

121 
121 
121 
120 
121 
II9 
120 
II9 

118 
119 
118 
118 
117 
118 
116 
117 
116 
116 
116 
"5 
"5 
"5 
"5 
114 
114 

"3 
114 

"3 

112 
II3 
112 
112 
112 
III 
III 
III 
1  10 
III 

no 
109 
no 
109 
109 
1  08 
109 
1  08 
1  08 
107 
108 
107 
106 
107 
106 
1  06 
106 
1  06 
105 
105 
105 
104 

0.97  838 
0.97  717 
0.97  596 
0.97  475 
0-97  355 

9.99  761 
9-99  76o 
9-99  759 
9-99  757 
9-99  756 

60 

59 
58 
57 
56 

6 

7 
8 
9 

10 

20 

3° 
40 

50 

6 

8 
9 

10 
20 

3° 

40 

50 

6 

7 
8 

9 
10 

20 

3° 
40 

So 

6 

7 
8 

9 

10 

20 

30 
40 

50 

6 

7 
8 

9 

10 
20 
30 
40 
50 

6 

8 
9 

10 
20 

30 

40 

50 

121 
I2.I 
I4.I 

16.1 
18.2 

20.2 

40-3 
00.5 
80.7 

100.8 
iiS 
11.8 
13-8 
15-7 
17.7 
19.7 
39-3 
59'° 
78.7 
98.3 
«5 
"•5 
13-4 
15-3 
17-3 
19.2 
38.3' 
57-5 
76.7 
95-8 

112 
II.  2 

I3-I 
14.9 

16.8 
18.7 
37-3 
56.0 

74-7 
93-3 
109 
10.9 
12.7 
14-5 
16.4 
18.2 
36.3 
54-5 
72.7 
90.8 

106 
10.6 
12.4 
14.1 

15-9 
17.7 

35-3 
53-0 
70.7 
88.3 

120 
I2.C 

I4.c 
i6.c 
i8.c 

20.C 

40.c 
6o.c 
8o.c 

IOO.C 

117 
11.7 
13-7 
15-6 
17.6 
19-5 
39-o 
58.5 
78.0 

97-5 
114 
11.4 
13-3 
15-2 
17.1 
19.0 
38.0 
57-0 
76.0 
95-0 
in 
n.  i 
13-0 
14.8 
!6.7 
18.5 
37-0 
55-5 
74.0 

92.5 
108 
10.8 

12.6 

14.4 
16.2 
18.0 
36.0 
54-0 
72.0 
90.0 

105 

io-5 
12.3 
14.0 
15-8 
17-5 
35-0 
52.5 
70.0 

87.5 

iig 

>    11.9 
>    13-9 
>    15-9 
>    17-9 
)    19.8 

>    39-7 
>    59-5 
>    79-3 
>    99-2 

116 
11.6 
13-5 
15-5 
17-4 
19-3 
38.7 
58.0 
77-3 
96.7 

113 

"•3 

13.2 

15-1 
17.0 
18.8 
37-7 
56.5 
75-3 
94.2 

'no 

II.O 
12.8 

14-7 
16.5 
18.3 
36.7 
55-0 
73-3 
91.7 

107 
10.7 
12.5 
14-3 
16.1 
17-8 
35-7 
53-5 
71-3 
89.2 

104 
10.4 

12.  1 

13-9 
15-6 
17-3 

34-7 
52.0 

69-3 
86.7 

I 

7 
8 
9 

9.02  520 
9.02  639 
9.02  757 
9.02  874 
9.02  992 

9.02  766 
9.02  885 
9.03  005 
9.03  124 
9.03  242 

0.97  234 
0.97  115 
0.96  995 
0.96  876 
0.96  758 

9-99  755 
9-99  753 
9-99  752 
9-99  75i 
9-99  749 

55 
54 
53 
52 
5i 

1O 

ii 

12 
13 
14 

9.03  109 
9.03  226 
9-03  342 
9-03  458 
9-03  574 

9.03  361 
9-03  479 
9-03  597 
9.03  714 
9.03  832 

0.96  639 
0.96  521 
0.96  403 
0.96  286 
0.96  168 

9-99  748 
9-99  747 
9-99  745 
9-99  744 
9-99  742 

5O 

49 
48 
47 
46 

15 

16 
17 
18 

19 

9.03  690 
9.03  805 
9.03  920 
9.04  034 
9.04  149 

9.03  948 
9.04  065 
9.04  181 
9.04  297 
9.04  413 

0.96  052 

o-95  935 
0.95  819 

0-95  703 
0-95  587 

9-99  74i 
9-99  74° 
9-99  738 
9-99  737 
9-99  736 

45 
44 
43 
42 
41 

20 

21 
22 
23 
24 

9.04  262 
9.04  376 
9.04  490 
9.04  603 
9-04  715 

9.04  528 
9.04  643 
9.04  758 
9.04  873 
9.04  987 

0.95  472 

0-95  357 
0.95  242 
0.95  127 
0.95  013 

9-99  734 
9-99  733 
9-99  731 
9-99  730 
9-99  728 

40 

39 
38 
37 
36 

25 
26 

27 
28 

29 

9.04  828 
9.04  940 
9.05  052 
9.05  164 
9-05  275 

9.05  101 
9-05  214 
9.05  328 
9.05  441 
9-05  553 

0.94  899 
0.94  786 
0.94  672 

o-94  559 
0.94  447 

9-99  727 
9-99  726 
9.99  724 
9-99  723 
9-99  721 

35 
34 
33 
32 
3i 

30 

3i 
32 
33 
34 

9.05  386 

9-05  497 
9.05  607 
9.05  717 
9-05  827 

9.05  666 
9.05  778 
9-05  890 

9.06  002 
9.06  113 

o-94  334 

0.94  222 

0.94  no 

0.93  998 
0.93  887 

9.99  720 
9-99  7i8 
9.99  717 
9-99  7i6 
9  99  714 

30 

29 

28 
27 
26 

11 

37 
38 
39 

9-05  937 
9.06  046 
9-o6  155 
9.06  264 
9.06  372 

9.06  224 

9-o6  335 
9.06  445 
9.06  556 
9.06  666 

0.93  776 
0.93  665 

o-93  555 
0-93444 
0-93  334 

9-99  713 
9.99711 
9-99  7io 
9-99  708 
9-99  707 

25 
24 
23 

22 
21 

4O 

4i 
42 
43 
44 

9.06  481 
9-o6  589 
9.06  696 
9.06  804 
9.06  911 

9.06  775 
9.06  885 
9.06  994 
9.07  103 
9.07  211 

0.93  225 

o-93  "5 
0.93  006 
0.92  897 
0.92  789 

9-99  705 
9-99  704 
9-99  702 
9-99  7°i 
9.99  699 

20 

19 

18 

17 
16 

45 
46 

47 
48 
49 

9.07  018 
9.07  124 
9.07  231 

9-07  337 
9.07  442 

9.07  320 
9.07  428 
9-07  536 
9.07  643 

9-07  751 

0.92  680 
0.92  572 
0.92  464 
0-92  357 
0.92  249 

9-99  698 
9-99  696 
9-99  695 
9-99  693 
9-99  692 

15 
14 
13 

12 

II 

50 

Si 
52 
53 
54 

9.07  548 
9-07  653 
9-°7  758 
9.07  863 
9.07968 

105 
105 
105 
105 

9.07  858 
9.07  964 
9.08  071 
9.08  177 
9.08  283 

0.92  142 
0.92  036 
0.91  929 
0.91  823 
0.91  717 

9.99690 
9.99  689 

9-99  687 
9.99  686 
9.99  684 

10 

9 
8 
7 
6 

P 

57 
58 
59 

9.08  072 
9.08  176 
9.08  280 
9.08  383 
9.08  486 

104 
104 
103 
103 
103 

9-o8  389 
9.08  495 
9.08  600 
9.08  705 
9.08  810 

0.91  611 

0-91  505 
0.91  400 
0.91  295 
0.91  190 

9-99  683 
9.99  681 
9.99  680 
9-99  678 
9-99  677 

5 
4 
3 

2 
I 

60 

9.08  589 

9.08  914 

0.91  086 

9-99  675 

0 

L.  COM.      d. 

L.  Cotg.  c.  d.  L.Tang. 

L.  Sin. 

f 

Prop.  Pts. 

83( 


29 


/• 

L.  Sin. 

d. 

JL.Tang. 

c.  d. 

L.Cotg. 

L.  Cos. 

Prop 

.  Pts 

0 

I 

2 

3 
4 

9.08  589 
9.08  692 
9.08  795 
9.08  897 
9.08  999 

103 
103 

102 
IO2 

9.08  914 
9.09  019 
9.09  123 
9.09  227 
9.09  330 

105 
104 
104 
103 

0.91  086 
0.90  981 
0.90  877 
0.90  773 
0.90  670 

9-99  675 
9.99  674 

9-99  672 
9.99  670 
9.99  669 

60 

59 
58 
57 
56 

6 

7 
8 

105 
10.5 
12.3 
14.0 

104 
10.4 

12.  1 
13-9 

103 
10.3 
I2.O 
13-7 

5 
6 

7 
8 
9 

9.09  101 

9.09  202 
9.09  304 
9.09  405 
9.09  506 

OI 
O2 
OI 
OI 

9.09  434 

9-°9  537 
9.09  640 
9.09  742 
9.09  845 

103 
103 

IO2 

103 

0.90  566 
0.90  463 
0.90  360 
0.90  258 
0.90  155 

9.99  667 
9.99  666 
9.99  664 
9.99  663 
9.99  661 

55 
54 
53 
52 
5i 

9 
10 

20 

30 
40 
CQ 

15.8 
17.5 
35-0 

52-5 
70.0  j 
87  <; 

15-6 
17-3 
34-7 
52.0 

69.3 

86  7 

15-5 
17.2 

34-3 

51-5 
68.7 
8c  8 

10 

ii 

12 
13 
14 

9.09  606 
9.09  707 
9.09  807 
9.09  907 
9.IO  OO6 

101 
IOO 
IOO 

99 

9.09  947 
9.10  049 
9.10  150 
9.10  252 
9-10  353 

102 
101 
102 
IOI 

0.90  053 
0.89  951 
0.89  850 
0.89  748 
0.89  647 

9-99  659 
9.99  658 

9-99  656 
9-99  655 
9-99  653 

5O 

49 
48 
47 
46 

6 

7 
8 

102 
IO.2 
II.9 
13-6 

IOI 
IO.I 

n.8 
13-5 

zoo 

IO.O 

11.7 
13.3 

15 

16 
17 
18 
19 

9.10  106 
9.10  205 
9.10  304 
9.10  402 
9.10  501 

99 
99 
98 

99 

9.10  454 

9-i°  555 
9.10  656 
9.10  756 
9.10  856 

IOI 
IOI 
IOO 
IOO 

0.89  546 
0.89  445 
0.89  344 
0.89  244 
0.89  144 

9.99  651 
9-99  650 
9.99  648 
9.99  647 
9-99  645 

45 
44 
43 
42 
41 

9 

10 
20 

30 

40 

15-3 
17.0 

34-0 
51.0 
68.0 
85  o 

15-2 
16.8 
33-7 
50.5 
67-3 

8d  2 

15.0 

16.7 

33-3 
50.0 
66.7 

8-3  q 

20 

21 
22 
23 
24 

9.10  599 
9.10  697 
9.10  795 
9.10  893 
9.10  990 

98 
98 
98 
98 
97 

9.10  956 
9.11  056 

9-ii  155 
9.11  254 

9-  "  353 

IOO 

99 
99 
99 

0.89  044 
0.88  944 
0.88  845 
0.88  746 
0.88  647 

9-99  643 
9-99  642 
9.99  640 
9-99  638 
9-99  637 

4O 

39 
38 
37 
36 

6 
8 

99 

9.9 
ii.  6 
13.2 

98 

9-8 
11.4 
I3-I 

97 
9-7 
«.3 
12.9 

25 
26 

27 
28 
29 

9.11  087 
9.11  184 
9.11  281 
9.11  377 
9.11  474 

97 
97 
97 
96 

97 
nfi 

9.11  452 

9-ii  551 
9.11  649 
9.  1  1  747 
9.  1  1  845 

99 

99 
98 
98 
98 
08 

0.88  548 
0.88  449 
0.88  351 
0.88  253 
0.88  155 

9-99  635 
9-99  633 
9.99  632 

9-99  630 
9-99  629 

35 
34 
33 
32 
3i 

9 

10 
20 
30 
40 

14.9 
16.5 
33-0 
49-5 
66.0 
82  c; 

14.7 
16.3 
32.7 
49.0 

65-3 
81  7 

14.6 
16.2 
32.3 
48.5 
64.7 
80  8 

3O 

3i 

32 
33 
34 

9.11  570 
9  ii  666 
9.11  761 
9.11  857 
9.11  952 

9° 
96 
95 
96 
95 

9-  1  1  943 
9.12  040 
9.12  138 
9.12  235 
9.12  332 

9° 

97 
98 

97 
97 
06 

0.88  057 
0.87  960 
0.87  862 
0.87  765 
0.87  668 

9.99  627 
9-99  625 
9-99  624 
9.99  622 
9.99  620 

30 

29 
28 
27 
26 

6 

7 
8 

96 
9-6 

II.  2 
12.8 

95 

9-5 
n.  I 
12.7 

94 

9-4 

II.O 

12.5 

P 

37 
38 
39 

9.12  047 
9.12  142 
9.12  236 
9.12  331 
9.12  425 

95 
95 
94 
95 
94 

9.12  428 
9.12  525 
9.12  621 
9.12717 
9.12  813 

9° 

97 
96 
96 
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0.87  572 
0.87  475 
0.87  379 
0.87  283 
0.87  187 

9.99  618 
9.99  617 
9-99  615 
9-99  613 
9.99  612 

25 
24 
23 

22 
21 

9 
10 

20 

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43 
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9.12519 
9.12  612 
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94 
93 
94 
93 
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9.12  909 
9.13  004 
9.13  099 

9-13  194 
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95 
95 
95 
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0.87  091 
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0.86  806 
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9.99  610 
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20 

19 
18 
17 
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45 
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47 
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9.12  985 
9.13  078 
9.13  171 
9.13  263 
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93 
93 
93 
92 
92 

9-!3  384 
9.13  478 

9.13  573 
9.13  667 
9.13  761 

95 
94 
95 
94 
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0.86  616 
0.86  522 
0.86  427 
0.86  333 
0.86  239 

9.99  601 
9.99  600 

9-99  598 
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9-99  595 

15 
14 
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12 
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9 
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52 
53 
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9-13  447 
9-13  539 
9.13  630 
9.13  722 
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92 
92 

91 
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9-i3  854 
9.13  948 
9  14  041 

9-14  134 
9.14  227 

93 
94 
93 
93 
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0.86  146 
0.86  052 
0.85  959 
0.85  866 
0.85  773 

9-99  593 
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9.13  904 

9-13  994 
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9-14  175 
9.14  266 

91 
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91 
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9.14  320 
9.14  412 
9.14  504 
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93 
92 
92 
93 
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0.85  680 
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0.85  496 
0.85  403 
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9.15  236 
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0.84  764 
0.84  673 
0.84  583 
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9-99  566 
9-99  565 
9-99  563 
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55 
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9-i5  245 
9-15  333 
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9.15  688 

9-15  777 
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9-15  956 
9.16  046 

0.84  312 
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0.84  044 

0-83  954 

9-99  557 
9-99  556 
9-99  554 
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50 

49 
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47 
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15 
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17 
18 
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9-15  683 
9.15  770 
9-15  857 
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9.16  030 

9-i6  135 
9.16  224 
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0.83  865 
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0-83  599 
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9-99  548 
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9-99  545 
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45 
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43 
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20 

21 
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23 
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9.16  116 
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9.16  577 
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9.16  841 
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0.83  423 

0-83  335 
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0.83  159 
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9-99  539 
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40 

39 
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25 
26 

27 

28 
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9-i6  545 
9.16  631 
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9.16  886 

9.17  016 
9.17  103 
9.17  190 
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0.82  984 
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0.82  723 
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9-99  530 
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35 
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9.16  970 

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9-99  520 
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30 

29 
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27 
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35 
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9.17  391 
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0.81  864 
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9.99  511 
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0.81  694 
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0.81  272 
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9.99  492 
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9.19  146 
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0.79  218 
0.79  138 
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0.78  978 
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9-99  442 
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0-77  795 
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9.99  411 

9-99  409 
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9.99  404 
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35 
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30     36 
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9.21  761 
9.21  836 
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9.22  062 

9.22  361 
9.22  438 
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9-22  593 
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0.77  639 
0.77  562 
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9.99  400 
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9-99  396 
9-99  394 
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30 

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9.22  137 

9-22  211 
9-22  286 
9-22  361 

9-22  435 

9.22  747 
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0.77  253 
0.77  176 
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9.99  390 
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9-99  385 
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9.23  283 
9-23  359 
9-23  435 

0.76  870 
0.76  794 
0.76  717 
0.76  641 
0.76  565 

9-99  379 
9-99  377 
9-99  375 
9.99  372 
9-99  370 

20 

19 
18 
17 
16 

45 
46 

47 
48 

49 

9.22  878 
9.22  952 
9.23  025 
9.23  098 
9.23  171 

9.23  510 
9.23  586 
9.23  661 

9-23  737 
9.23  812 

0.76  490 
0.76  414 
0.76  339 
0.76  263 
0.76  188 

9-99  368 
9-99  366 
9-99  364 
9.99  362 

9-99  359 

15 
14 

13 

12 
II 

50 

Si 
52 
53 
54 

9.23  244 

9-23  317 
9.23  390 
9.23  462 

9-23  535 

9-23  887 
9.23  962 
9.24  037 

9.24  112 

9.24  186 

0.76  113 
0.76  038 

o.75  963 
0.75  888 

0.75  814 

9-99  357 
9-99  355 
9-99  353 
9-99  35i 
9-99  348 

10 

9 
8 

6 

55 
56 
57 
58 
59 

9.23  607 
9.23  679 
9-23  752 
9.23  823 

9-23  895 

9.24  261 

9-24  335 
9.24  410 
9.24  484 
9-24  558 

0.75  739 
0.75  665 
0-75  590 
0-75  5i6 
0.75  442 

9.99  346 
9-99  344 
9-99  342 
9.99  340 

9-99  337 

5 
4 
3 

2 
I 

60 

9.23  967 

9.24  632 

0.75  368 

9-99  335 

0 

JL.  Cos. 

d. 

L,.  Cotg. 

C.  d. 

L.Tang. 

L.  Sin. 

/• 

Prop.  Pts. 

8OC 


10' 


r 

L.  Sin. 

d. 

L.Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

Pi 

op.  1 

*ts. 

0 

I 

2 

3 
4 

9.23  967 
9.24  039 
9.24  no 
9.24  181 
9-24  253 

72 
71 
7* 
72 

9.24  632 
9.24  706 
9.24  779 

9-24  853 
9.24  926 

74 
73 
74 
73 

0.75  368 
0.75  294 

0.75  221 
0-75  147 

o.7S  074 

9-99  335 
9-99  333 
9-99  331 
9.99  328 
9-99  326 

2 
2 

3 

2 

60 

59 
58 
57 
56 

6 

7 
8 

74 

7-4 
8.6 

9-9 

73 

7-3 
8-5 
9-7 

5 
6 

7 
8 
9 

9.24  324 

9-24  395 
9.24  466 

9-24  536 
9.24  607 

71 
7i 
7i 
70 
7i 

9.25  ooo 
9-25  073 
9.25  146 
9-25  219 
9.25  292 

74 
73 
73 
73 
73 

0.75  ooo 
0.74  927 

0.74  854 
9.74  781 
0.74  708 

9-99  324 
9-99  322 
9-99  319 
9-99  3J7 
9-99  315 

2 

3 

2 
2 

55 
54 
53 
52 
51 

y 

10 
20 

30 
40 

CO 

II.  I 
12.3 

24.7 
37-0 
49-3 

6l  7 

n.o 

12.2 
24-3 
36.5 
48.7- 

60  8 

10 

ii 

12 
13 
14 

9.24  677 
9.24  748 
9.24  818 
9.24  888 
9.24  958 

70 

7i 
70 

TO 
70 

9-25  365 
9-25  437 
9-25  5io 
9-25  582 
9-25  655 

73 
72 

73 
72 

73 

0.74  635 

0.74  563 
0.74  490 
0.74  418 
0.74  345 

9-99  313 
9.99  310 
9-99  308 
9-99  306 
9-99  3°4 

3 

2 
2 
2 

50 

49 
48 
47 
46 

6 
8 

72 

7.2 

8.4 

9.6 

7i 
7-1 
8-3 

9-5 

15 

16 
17 

18 

19 

9.25  028 
9.25  098 
9.25  168 
9-25  237 
.9-25  307 

70 
70 
69 
70 
fm 

9.25  727 

9-25  799 
9.25  871 

9-25  943 
9.26  015 

72 
72 
72 
72 
72 

0.74  273 

0.74  201 
0.74  129 
0.74  057 
0-73  985 

9.99  301 
9.99  299 
9-99  297 
9-99  294 
9-99  292 

3 

2 
2 

3 

2 

45 
44 
43 
42 
4i 

9 

10 
20 

30 

40 

CQ 

10.8 

12.0 
24.0 
36.0 
48.0 

60  o 

10.7 
11.8 
23-7 

35-5 
47-3 

20 

21 
22 

23 
24 

9-25  376 
9-25  445 
9-25  514 
9-25  583 
9.25  652 

09 
69 
69 
69 
69 

9.26  086 
9.26  158 
9.26  229 
9.26  301 
9.26  372 

71 
72 

7i 
72 

7i 

0-73  9M 
0.73  842 
0.73  771 
0.73  699 
0.73  628 

9.99  290 
9.99  288 
9-99  285 
9-99  283 
9.99  281 

2 

3 

2 
2 

40 

39 
38 

1 

6 

7 

8 

70 

7.0 

8.2 

9-3 

69 

6.9 
8.1 
9-2 

5 

27 
28 
29 

9-25  721 
9.25  790 
9.25  858 
9.25  927 
9-25  995 

°9 
69 
68 

69 

68 
68 

9.26  443 
9.26  514 
9.26  585 
9.26  655 
9.26  726 

71 
71 
7i 
70 
7i 

o.73  557 
0.73  486 

0-73  415 
0-73  345 
0.73  274 

9-99  278 
9.99  276 
9.99  274 
9-99  271 
9-99  269 

2 

2 

3 

2 

35 
34 
33 
32 
.31 

y 

10 
20 
30 
40 

CQ 

10.5 
11.7 
23-3 
35-o 
46.7 

cR  q 

10.4 

"•5 

23.0 

34-5 
46.0 

C,7  e 

30 

3i 
32 
33 
34 

9.26  063 
9.26  131 
9.26  199 
9.26  267 
9-26  335 

68 
68 
68 
68 
68 

9.26  797 
9.26  867 
9.26  937 
9.27  008 
9.27  078 

70 
70 

7i 
70 

0.73  203 

0-73  133 
0.73  063 
0.72  992 
0.72  922 

9-99  267 
9.99  264 
9.99  262 
9.99  260 
9-99  257 

3 

2 

2 

3 

30 

29 
28 

27 

26 

6 
7 
8 

68 
6.8 
7-9 
9-i 

67 

6-7 
7-8 
8.9 

35 
36 
37 
38 
39 

9.26  403 
9.26  470 
9.26  538 
9.26  605 
9.26  672 

67 
68 
67 
67 

£.- 

9.27  148 
9.27  218 
9.27  288 

9-27  357 
9.27  427 

70 
70 
70 
69 
70 

0.72  852 
0.72  782 
0.72  712 
0.72  643 
0.72  573 

9-99  255 
9-99  252 
9-99  250 
9-99  248 
9-99  243 

3 

2 

2 

3 

25 
24 
23 

22 
21 

9 

10 
20 

30 
40 

IO.2 

"•3 
22.7 
34-0 
45-3 
c.6  7 

IO.I 
II.  2 
22.3 

33-5 
44-7 

re  8 

40 

4i 
42 
43 
44 

9.26  739 
9.26  806 
9.26  873 
9.26  940 
9.27  007 

O7 

67 

67 
67 
67 

9.27  496 
9.27  566 
9-27  635 
9-27  704 
9.27  773 

09 
70 
69 
69 
69 

0.72  504 
0.72  434 
0.72  365 
0.72  296 
0.72  227 

9-99  243 
9-99  241 
9-99  238 
9-99  236 
9-99  233 

2 

3 

2 

3 

20 

19 
18 

17 
16 

6 
7 
8 

66 
6.6 

7-7 
8.8 

65 

6-5 
7.6 

8-7 

45 
46 

47 
48 
49 

9.27  073 
9.27  14° 
9.27  206 
9.27  273 
9-27  339 

67 

66 
67 
66 

9.27  842 
9.27  911 
9.27  980 
9.28  049 
9.28  117 

69 
69 
69 
69 
68 

0.72  158 
0.72  089 

0.72  020 
0.71  951 
0.71  883 

9-99  231 
9-99  229 
9.99  226 
9-99  224 
9.99  221 

2 

3 

2 

3 

IS 
14 
13 

12 

II 

9 

10 

20 
30 
40 

y-y 

n.o 

22.0 

S3-0 

44.0 

9.8 
10.8 
21.7 
32.5 
43-3 

5O 

5i 
52 
53 
54 

9x27  405 
9.27  471 

9-27  537 
9.27  602 
9.27  668 

66 
66 

65 
66 

9.28  186 
9.28  254 
9.28  323 
9-28  391 
9.28  459 

69 
68 
69 
68 
68 

0.71  814 
0.71  746 
0.71  677 
0.71  609 
0.71  541 

9-99  219 
9-99  217 
9-99  214 
9.99  212 
9-99  209 

2 

3 

2 

3 

10 

9 
8 

7 
6 

ou 

6 

\7 

8 

33-v 
3 

0-3 
0.4 
0.4 

a 

0.2 
O.2 
0-3 

55 
56 
57 
58 
59 

9-27  734 
9.27  799 
9.27  864 
9.27  930 
9-27  995 

65 
65 
66 
65 

9.28  527 
9-28  59? 
9.28  662 
9.28  730 
9.28  798 

68 
67 
63 
68 
fit 

0.71  473 
0.71  405 
0.71  338 
0.71  270 
0.71  202 

9-99  207 
9.99  204 
9.99  202 
9.99  200 
9-99  197 

3 

2 
2 

3 

5 

4 
3 

a 
i 

9 

10 
20 

30 
40 

0-5 
0-5 
z.o 
1-5 

2.0 
2  ^ 

0-3 
0-3 
0.7 
1.0 

i-3 

I  7 

GO 

9.28  060 

°5 

9.28  865 

07 

0.71  135 

9-99  195 

0 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.TniiK. 

L.  Sin. 

d. 

r 

Pr 

op.  1 

Ms. 

79< 


11' 


33 


/• 

L.  Sin. 

d. 

L.Tang. 

c.  d.!  L.  Cotg. 

L.  Cos. 

d. 

Prop.  Pts. 

o 

I 

2 

3 

4 

9.28  060 
9.28  125 
9.28  190 
9.28  254 
9.28  319 

65 
65 
64 

65 
65 
64 
64 
65 
64 
64 
64 
64 

63 
64 
64 

63 
63 
64 
63 
63 
63 
63 
63 
62 

9.28  865 
9-28  933 
9.29  ooo 
9.29  067 

9.29  134 

68 
67 
67 
67 
67 
67 
67 
67 
66 
67 
66 
67 
66 
66 
66 
66 
66 
66 
66 
65 
66 
65 
65 
66 
65 
65 
65 
65 
65 
64 

65 
64 
65 
64 
64 

65 
64 
64 
64 
64 

63 
64 

63 
64 

63 
64 
63 
63 
63 
63 
63 
63 
63 
62 
63 
62 

63 
62 
62 
62 

0-71  135 
0.71  067 
0.71  ooo 
0.70  933 
0.70  866 

9-99  195 
9.99  192 
9.99  190 
9.99  187 
9.99  185 

3 

2 

3 

2 

3 

2 

3 

2 

3 

2 

3 

2 

3 

2 

3 

2 

3 

2 

3 

2 

3 

2 

,3 
2 

3 

2 

3 
3 

2 

3 

2 

3 

2 

3 
3 

2 

3 

2 

3 
3 

2 

3 

2 

3 
3 

2 

3 
3 

2 

3 
3 

2 

3 
3 

2 

3 
3 

2 

3 
3 

60 

59 
58 
57 
56 

6 

7 
8 

9 

10 
20 

30 
40 

50 

6 

7 
8 

9 

10 
"20 

3° 

40 
50 

6 

7 
8 

9 

10 
20 

30 
40 
50 

6 

7 
8 

9 

10 
20 

30 
40 

50 

6 
7 
8 

9 

10 

20 

30 
40 

50 

6 

8 
9 

10 
20 

30 
40 

50 

68 

6.8 
7-9 
9-i 

10.2 

"•3 

22.7 

34-° 

45-3 
56.7 
66 
6.6 
7-7 
8.8 
9-9 

II.O 
22.0 

33-° 

44.0 
55.0 
64 

6.4 
7-5 
8-5 
9.6 
10.7 
21.3 
32.0 
42.7 
53-3 
62 

6.2 

7.2 
8-3 
9-3 
10.3 
20.7 
31.0 
41-3 
51-7 
60 
6.0 
7.0 
8.0 
9.0 

IO.O 
20.0 
30.0 
4O.O 
50.0 

3 

o-3 
0.4 
0.4 
0.5 
o.S 

I.O 

Jt-S 

2.0 
2.5 

67 

6-7 
7.8 
8.9 

10.  1 
II.2 
22.3 

33-5 

44-7 
55-8 

65 

6-5 
7.6 
8.7 
9-8 
10.8 
21.7 
32.5 
43-3 
54-2 

63 
6-3 
7-4 
8.4 

9-5 
10.5 

21.0 

31-5 
42.0 

52.5 
61 
6.1 

7-1 
8.1 
9-2 

10.2 
20.3 

30.5 
40.7 
50.8 

59 

5-9 
6-9 
7-9 
8.9 
9.8 
19.7 
29-5 
39-3 
49.2 

2 
0.2 
0.2 
0-3 

°-3 
0-3 

0.7 

I.O 

i-3 
1-7 

6 
.7 
8 
'9 

9.28  384 
9.28  448 
9.28  512 
9.28  577 
9.28  641 

9.29  2OI 
9.29  268 

9-29  335 
9.29  402 
9.29  468 

0.70  799 
0.70  732 
0.70  665 
0.70  598 
0.70  532 

9.99  182 
9.99  180 
9.99  177 

9-99  175 
9.99  172 

55 
54 
53 
52 
5i 

10 

ii 

12 

13 
14 

9.28  705 
9.28  769 
9.28  833 
9.28  896 
9.28  960 

9-29  535 
9.29  601 
9.29  668 

9-29  734 
9.29  800 

0.70  465 

.0-7°  399 
0.70  332 
0.70  266 
0.70  200 

9.99  170 
9.99  167 
9.99  165 
9.99  162 
9.99  160 

50 

49 
48 

47 
46 

15 

16 

17 

18 

19 

9.29  024 
9.29  087 

9-29  150 
9.29  214 
9.29  277 

9.29  866 
9.29  932 
9.29  998 
9.30  064 
9.30  130 

0.70  134 
0.70  068 

0.70  002 
0.69  936 
0.69  870 

9-99  157 
9-99  155 
9.99  152 

9-99  ISO 
9.99  147 

45 
44 
43 
42 

4i 

20 

21 
22 
23 

24 

9.29  340 
9.29  403 
9.29  466 
9.29  529 
9.29  591 

9-3°  195 
9.30  261 
9.30  326 
9-30  391 
9-30  457 

0.69  805 

0.69  739 
0.69  674 
0.69  609 
0-69  543 

9-99  145 
9-99  142 
9-99  140 
9-99  137 
9-99  135 

40 

39 
38 
37 
36 

25 
26 

27 
28 

29 

9.29  654 
9.29  716 
9.29  779 
9.29  841 
9.29  903 

°3 
62 

63 
62 
62 

9.30  522 
9-30  587 
9.30  652 
9.30  717 
9.30  782 

0.69  478 
0.69  413 
0.69  348 
0.69  283 
0.69  218 

9-99  132 
9-99  130 
9-99  127 
9.99  124 
9.99  122 

35 
34 
33 
32 
3i 

30 

3i 
32 
33 
34 

9.29  966 
9.30  028 
9.30  090 

9-30  151 
9.30  213 

°3 
62 
62 
61 
62 

9.30  846 
9.30  911 
9-30  975 
9.31  040 
9.31  104 

0.69  154 
0.69  089 
0.69  025 
0.68  960 
0.68  896 

9.99  119 
9.99  117 
9.99  114 
9.99  112 
9.99  109 

30 

29 
28 
27 
26 

11 

37 
38 
39 

9-30  275 
9-30  336 
9-30  398 
9-30  459 
9.30  521 

61 
62 
6x 
62 
61 
61 
61 
61 
61 
61 
60 
61 
60 
61 
60 
61 
60 
60 
60 
60 

59 
60 
60 

59 
60 

9.31  168 
9-31  233 
9.31  297 
9.31  361 
9-31  425 

0.68  832 
0.68  767 
0.68  703 
0.68  639 
0.68  575 

9.99  106 

9-99  104 
9.99  101 
9.99  099 
9.99  096 

25 
24 

23 

22 
21 

40 

4i 

42 
43 
44 

9.30  582 
9-30  643 
9.30  704 

9-30  765 
9.30  826 

9.31  489 
9-3i  552 
9.31  616 
9.31  679 
9-31  743 

0.68  511 
0.68  448 
0.68  384 
0.68  321 
0.68  257 

9.99  093 

9-99  °9i 
9.99  088 
9.99  086 
9.99  083 

2O 

19 

18 

17 
16 

45 
46 

47 
48 

49 

9.30  887 

9-30  947 
9.31  008 
9.31  068 
9.31  129 

9.31  806 
9.31  870 

9-3i  933 
9.31  996 
9-32  059 

0.68  194 
0.68  130 
0.68  067 
0.68  004 
0.67  941 

9.99  080 
9-99  078 
9-99  075 
9-99  072 
9.99  070 

IS 

14 
13 

12 
II 

50 

5i 
52 
53 
54 

9.31  189 
9.31  250 
9.31  310 
9-31  370 
9-3i  430 

9.32  122 
9.32  185 
9.32  248 
9.32  311 

9-32  373 

0.67  878 
0.67  815 
0.67  752 
0.67  689 
0.67  627 

9.99  067 
9.99  064 
9.99  062 

9-99  059 
9.99  056 

10 

9 
8 

6 

55 
56 
57 
58 
59 

9.31  490 

9-3i  549 
9.31  609 
9.31  669 
9.31  728 

9-32  436 
9.32  498 
9.32  561 
9.32  623 
9.32  685 

0.67  564 
0.67  502 
0.67  439 
0.67  377 
0.67  315 

9-99  054 
9.99  051 
9.99  048 
9.99  046 
9-99  043 

5 
4 
3 

2 

I 

60 

9.31  788 

9-32  747 

0.67  253 

9.99  040 

0 

L.  Cos. 

d. 

L.  Cotg.  c.  d. 

L.Tang. 

L.  Sin. 

d. 

/• 

Prop.  Pts. 

78( 


34 


/• 

1  .  Sin. 

d. 

L.Taug.  c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

Prop.  Pts. 

0 

I 

2 

3 

4 

9.31  788 
9.31  847 
9.31  907 
9.31  966 
9.32  025 

59 
60 

59 
59 
59 
59 
59 
59 
58 
59 
59 
58 
58 
59 
58 
58 
58 
58 
58 
58 
58 
57 
58 
57 
58 

57 
57 
58 
57 
57 
57 
56 
57 
57 
57 
56 
57 
56 
56 
57 
56 
56 
56 
56 
56 
56 
55 
56 
55 
56 
55 
56 
55 
55 
55 
55 
55 
55 
55 

9-32  747 
9.32  810 
9-32  872 
9-32  933 
9-32  995 

63 
62 
61 
62 
62 
62 
61 
62 
61 
62 
61 
61 
61 
61 
61 
61 
61 
61 
60 
61 
60 
61 
60 
60 
61 
60 
60 
60 
60 
60 

59 
60 
60 
59 
60 

59 
59 
59 
60 

59 
59 
59 
59 
58 
59 
59 
58 
59 
58 
59 
58 
58 
58 
58 
58 
58 
58 
58 
58 
57 

0.67  253 
0.67  190 
0.67  128 
0.67  067 
0.67  005 

9.99  040 
9.99  038 
9-99  035 
9-99  032 
9-99  030 

2 

3 
3 

2 

3 
3 

2 

3 
3 
3 

2 

3 
3 
3 

2 

3 
3 
3 

2 

3 
3 
3 

2 

3 
3 
3 

2 

3 
3 
3 
3 

2 

3 
3 
3 
3 

3 

2 

3 
3 
3 
3 
3 

2 

3 
3 
3 
3- 
3 

60 

59 
58 
57 
56 

6 

7 
8 

63 

6-3 
7-4 
8.4 

62 

6.2 

7.2 
8-3 
93 
10.3 
20.7 
31-0 
41-3 
5i-7 
60 
6.0 
7.0 
8.0 
9.0 

10.0 
20.0 
3O.O 
40.0 
50.0 

9 
•9 
•9 
•9 
•9 
.8 

•7 
•5 
•3 

.2 

57 
5-7 
6-7 
7-6 
8.6 

9-5 
19.0 
28.5 
38.0 
47-5 
55 

% 

7-3 
8-3 
9.2 
18.3 
27-5 
36.7 
45-8 

3 
0.2 
0.2 
0-3 
0-3 
0-3 
0.7 
I.O 

i-3 
1-7 

6 
7 

8 
9 

9.32  084 
9-32  M3 
9.32  202 
9.32  261 
9-32  319 

9-33  057 
9-33  H9 
9-33  180 
9-33  242 
9-33  303 

0.66  943 
0.66  881 
0.66  820 
0.66  758 
0.66  697 

9.99  027 
9.99  024 
9.99  022 
9.99  019 

9.99  016 

55 
54 
53 
52 
5i 

9 

10 
20 

3° 

40 

9-5 

10.5 

21.0 

31-5 
42.O 

52.5 

61 
6.1 

7-i 
8.1 
9-2 

10.2 
20.3 

30.5 
40.7 
50.8 

5 
6       e 
7      * 
8      7 

9     * 
10      9 

20     19 

30  29 

*o    35 
50    49 

58 
5-8 
6.8 
7-7 
8.7 
9-7 
19-3 
29.0 

38.7 
48.3 
56 
5-6 
6.5 

il 

93 
18.7 
28.0 

37-3 
46.7 

3 

0-3 
0.4 
0.4 
0-5 
0-5 

I.O 

i-5 

2.0 

3-5 

10 

ii 

12 
13 

14 

9-32  378 
9-32  437 
9-32  495 
9-32  553 
9.32  612 

9  33  365 
9-33  426 
9-33  487 
9-33  548 
9-33  609 

0.66  635 
0.66  574 
0.66  513 
0.66  452 
0.66  391 

9-99  013 
9.99  on 
9.99  008 
9-99  005 
9.99  002 

50 

49 
48 
47 
46 

5° 

6 

7 
8 

15 

16 

17 
18 
19 

9.32  670 
9.32  728 
9.32  786 
9.32  844 
9.32  902 

9-33  670 
9-33  731 
9-33  792 
9-33  853 
9-33  913 

0.66  330 
0.66  269 
0.66  208 
0.66  147 
0.66  087 

9.99000 
9.98  997 
9.98  994 
9.98  991 
9.98  989 

45 
44 
43 
42 
4i 

9 

10 
20 

3° 

40 

20 

21 
22 
23 

24 

9-32  960 
9.33  018 
9-33  075 
9-33  133 
9-33  190 

9-33  974 
9-34  °34 
9-34  °95 
9-34  155 
9-34  215 

0.66  026 
0.65  966 
0.65  905 
0.65  845 
0.65  785 

9.98  986 
9.98  983 
9.98  980 
9.98  978 
9-98  975 

4O 

39 
38 

| 

5° 

6 
7 
8 

9 

10 
20 
30 

40 
50 

6 

7 
8 

9 

10 
20 
30 
40 
50 

6 

7 
8 

9 

10 
20 
30 
40 
50 

25 
26 

27 
28 
29 

9-33  248 
9-33  305 
9-33  362 
9-33  420 
9-33  477 

9.34  276 
9-34  336 
9-34  396 
9-34  456 
9-34  5i6 

0.65  724 
0.65  664 
0.65  604 
0-65  544 
0.65  484 

9.98  972 
9.98  969 
9.98  967 
9.98  964 
9.98  961 

35 
34 
33 
32 
3i 

30 

3i 

32 
33 
34 

9-33  534 
9-33  59i 
9-33  647 
9-33  704 
9-33  76i 

9-34  576 
9-34  635 
9-34  695 
9-34  755 
9-34  814 

0.65  424 
0.65  365 
0.65  305 
0.65  245 
0.65  186 

9.98  958 
9-98  955 
9-98  953 
9.98  950 
9.98  947 

3O 

29 
28 

27 
26 

35 
36 

11 

39 

9-33  818 
9-33  874 
9-33  93i 
9-33  987 
9-34  043 

9-34  874 
9-34  933 
9-34  992 
9-35  051 
9-35  I" 

0.65  126 
0.65  067 
0.65  008 
0.64  949 
0.64  889 

9.98  944 
9.98  941 
9.98  938 
9.98  936 
9-98  933 

25 
24 
23 

22 
21 

40 

4i 

42 
43 
44 

9-34  ioo 
9-34  156 
9-34  212 
9-34  268 
9-34  324 

9-35  170 
9-35  229 
9-35  288 
9-35  347 
9-35  405 

0.64  830 
0.64  771 
0.64  712 
0.64  653 
0.64  595 

9.98  930 
9.98  927 
9.98  924 
9.98  921 
9.98  919 

20 

19 

18 

17 
16 

;t 

47 
48 
49 

9-34  38o 
9-34  436 
9-34  49i 
9-34  547 
9-34  602 

9-35  464 
9-35  523 
9-35  58i 
9-35  640 
9-35  698 

0.64  536 
0.64  477 
0.64  419 
0.64  360 
0.64  302 

9.98  916 
9.98  913 
9.98  910 
9.98  907 
9.98  904 

15 
14 
13 

12 
II 

:>o 

51 

52 

53 
54 

9-34  658 
9-34  713 
9-34  769 
9-34  824 
9-34  879 

9-35  757 
9-35  815 
9-35  873 
9-35  93i 
9-35  989 

0.64  243 
0.64  185 
0.64  127 
0.64  069 
0.64  on 

9.98  901 
9.98  898 
9.98  896 
9.98  893 
9.98  890 

3 

2 

3 
3 

10 

9 
8 

7 
6 

Cn  Cn  Cn  Cn  en 
\O  oovj  O\cn 

9-34  934 
9-34  989 
9-35  044 
9-35  099 
9-35  154 

9.36  047 
9.36  105 
9.36  163 
9.36  221 
9.36  279 

0.63  953 
0.63  895 
0.63  837 
0.63  779 

0.63  721 

9.98  887 
9.98  884 
9.98  881 
9.98  878 
9.98  875 

3 
3 
3 
3 
3 

5 
4 

3 

2 
I 

60 

,     -  .     - 

9-36  S36 

0.63  664 

9.98  872 

o 

L.  Cos.      d. 

L.  <  otg.  c.  d.  L.Tang. 

L.  Sin. 

d. 

r 

Prop.  Pts. 

77< 


35 


/• 

L.  Sin. 

d. 

L.Taug. 

c.  d 

L.  Cotg 

L.  Cos. 

d. 

P] 

rop. 

Pts. 

o 

I 

2 

3 
4 

9-35  209 
9-35  263 
9-35  3i8 
9-35  373 
9-35  427 

54 

55 
55 
54 

9-36  336 
9-36  394 
9-36  452 
9-36  509 
9.36  566 

58 
58 

57 
57 

eg 

0.63  664 
0.63  606 
0.63  548 
0.63  491 
0-63  434 

9.98  872 
9.98  869 
9.98  867 
9.98  864 
9.98  861 

3 

2 

3 
3 

GO 

59 
58 

57 
56 

6 
•7 
8 

58 

5-8 
6.8 
7-7 

57 

5-7 
6.7 
7-6 

5 
6 

7 
8 

9 

9-35  48i 
9-35  536 
9-35  590 
9-35  644 
9-35  698 

55 
54 
54 
54 

9.36  624 
9.36  681 
9-36  738 
9-36  795 
9.36  852 

57 
57 
57 
57 

0.63  376 
0.63  319 
0.63  262 
0.63  205 
0.63  148 

9.98  858 
9-98  855 
9-98  852 
9.98  849 
9.98  846 

3 
3 
3 
3 

55 
54 
53 
52 
5i 

9 

10 

20 
30 
40 

8.7 
9-7 
19-3 
29.0 

38.7 

/ifi  o 

8.6 

9-5 
19.0 
28.5 
38.0 

1O 

ii 

12 
13 
14 

9-35  752 
9-35  806 
9-35  860 
9-35  9H 
9-35  963 

54 
54 
54 
54 

9.36  909 
9.36  966 
9-37  023 
9-37  080 
9-37  137 

57 

57 
57 
57 

rfi 

0.63  091 
0.63  034 
0.62  977 
0.62  920 
0.62  863 

9.98  843 
9.98  840 
9.98  837 
9.98  834 
9.98  831 

3 
3 
3 

3 

50 

49 
48 

47 
46 

5° 

6 
7 
8 

4°  o 
56 
5-6 
6-5 
7-5 

47-5 
55 

5-5 
6.4 

7-3 

15 

16 

17 
18 

19 

9.36  022 
9-36  075 
9.36  129 
9.36  182 
9.36  236 

53 
54 
53 
54 

9-37  193 
9-37  250 
9-37  3°6 
9-37  363 
9-37  419 

57 

56 

57 
56 

0.62  807 
0.62  750 
0.62  694 
0.62  637 
0.62  581 

9.98  828 
9.98  825 
9.98  822 
9.98  819 
9.98  816 

3 
3 
3 
3 

45 
44 
43 
42 

4i 

9 

10 

20 
30 
40 

8.4 
9-3 
18.7 
28.0 

8-3 
9.2 
18.3 
27.5 
36.7 

A  C  8 

2O 

21 
22 

23 
24 

9.36  289 

9-36  342 
9-36  395 
9.36  449 
9.36  502 

53 
53 
54 
53 

9-37  476 
9-37  532 
9-37  588 
9-37  644 
9-37  700 

56 
56 
56 
56 
cfi 

0.62  524 
0.62  468 
0.62  412 
0.62  356 
0.62  300 

9.98  813 
9.98  810 
9.98  807 
9.98  804 
9.98  801 

3 
3 
3 
3 

4O 

39 
38 
37 
36 

Ou 

46.7 

5 

6      c 
7      ^ 
8      7 

45-° 
4 
4 
•3 
.2 

25 
26 
27 
28 
29 

9-36  555 
9.36  608 
9.36  660 

9-36  713 
9.36  766 

53 
52 
53 
53 

9-37  756 
9-37  812 
9-37  868 
9-37  924 
9-37  980 

56 
56 
56 
56 

0.62  244 
0.62  188 
0.62  132 
0.62  076 

0.62  020 

9.98  798 
9-98  795 
9.98  792 
9.98  789 
9.98  786 

3 

3 
3 
3 

35 
34 
33 
32 
3i 

, 

9      iJ 
[o      9 

20      18 

50  27 

(.0     36 

.1 
.O 
.0 
.0 
.0 

3O 

3i 
32 
33 

34 

9.36  819. 
9.36  871 
9.36  924 
9.36  976 
9-37  028 

52 
53 
52 
52 

9-38  035 
9-38  091 
9.38  147 

9.38  202 
9-38  257 

56 
56 

55 
55 

rf) 

0.61  965 
0.61  909 
0.61  853 
0.61  798 
0.61  743 

9.98  783 
9.98  780 
9.98  777 
9.98  774 
9.98  771 

3 
3 
3 
3 

30 

29 
28 
27 
26 

6 

7 
8 

>°    45 
53 
5-3 

6.2 

7-i 

5» 

5-2 

6.1 
6.9 

35 
36 
37 
38 
39 

9-37  081 
9-37  133 
9-37  185 
9-37  237 
9-37  289 

52 
52 
52 

52 

9-38  313 
9.38  368 
9-38  423 

9-38  479 
9-38  534 

55 
55 
56 
55 

0.61  687 
0.61  632 
0.61  577 
0.61  521 
0.61  466 

9.98  768 
9.98  765 
9.98  762 
9-98  759 
9.98  756 

3 
3 
3 
3 

25 
24 
23 

22 
21 

9 

10 
20 

3° 

40 

8.0 
8.8 
17.7 
26.5 
35-3 

7-8 
8-7 
17-3 
26.0 

34-7 

40 

4i 

42 
43 
44 

9-37  341 
9-37  393 
9-37  445 
9-37  497 
9-37  549 

52 
52 
52 
52 

9-38  589 
9.38  644 
9.38  699 
9-38  754 
9.38  808 

55 
55 
55 
54 

0.61  411 
0.61  356 
0.61  301 
0.61  246 
0.61  192 

9-98  753 
9.98  750 
9.98  746 
9-98  743 
9.98  740 

3 
4 
3 
3 

20 

19 

18 
17 
16 

5° 

6 

7 
8 

44.2 

5i 

5-i 
6.0 
6.8 

43-3 

4 

0.4 
0.5 
°-5 

45 
46 

47 
48 
49 

9-37  600 
9-37  652 
9-37  703 
9-37  755 
9-37  806 

52 
5i 
52 
5i 

9-38  863 
9.38  918 
9.38  972 
9-39  027 
9.39  082 

55 
54 
55 
55 

0.61  137 
0.61  082 
0.61  028 
0.60  973 
0.60  918 

9-98  737 
9-98  734 
9.98  731 
9.98  728 
9.98  725 

3 
3 
3 
3 

15 
14 
13 

12 
II 

9 

10 
20 

3° 

40 

7-7 
8-5 
17.0 

25.5 
34-0 

0.6 
0.7 
1-3 

2.0 
2.7 

50 

Si 
52 
53 
54 

9-37  858 
9-37  9°9 
9-37  960 
9.38  on 
9.38  062 

51 

5i 
Si 
5i 

9-39  I36 
9-39  19° 
9-39  245 
9-39  299 
9-39  353 

54 
54 

55 
54 
54 

0.60  864 
0.60  810 
0.60  755 
0.60  701 
0.60  647 

9.98  722 
9.98  719 
9-98  715 
9.98  712 
9.98  709 

3 
3 
4 
3 
3 

10 

9 
8 

7 
6 

5° 

6 

7 

8 

42.5 
3 

0.3 
0.4 
0.4 

3-3 

2 

0.2 
0.2 
0-3 

55 
56 
57 
58 
59 

9-38  113 
9.38  164 
9-38  215 
9.38  266 
9-38  317 

Si 
5i 
5i 
51 

9-39  407 
9-39  461 
9-39  515 
9-39  569 
9-39  623    j 

54 
54 
54 
54 

0.60  593 
0.60  539 
0.60  485 
0.60  431 
0.60  377 

9.98  706 
9.98  703 
9.98  700 
9.98  697 
9  98  694 

3 
3 
3 
3 
3 

5' 
4 
3 

2 
I 

9 

10 
20 

30 
40 

o-5 
0-5 

I.O 

1-5 

2.0 

0-3 
0-3 
0.7 

I.O 

i-3 

60 

9.38  368 

9-39  677 

54 

0.60  323 

9.98  690 

4 

0 

50 

2-5 

I-7 

L.  Cos. 

d. 

L.Cotg. 

c.  d. 

L.Tang. 

L.  Sin. 

d. 

/• 

Pr 

>|).   I 

•ts. 

76C 


r 

L.  Sin. 

d. 

L.Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

Pi 

op. 

Pts. 

0 

i 

2 

3 

4 

9.38  368 
9.38  418 
9.38  469 
9-38  519 
9-38  57o 

50 

51 
50 
5i 

9.39  677 
9-39  73i 
9-39  785 
9-39  838 
9.39  892 

54 
54 
53 
54 

0.60  323 
0.60  269 
0.60  215 
0.60  162 
0.60  108 

9.98  690 
9.98  687 
9.98  684 
9.98  681 
9.98  678 

3 
3 
3 
3 

GO 

59 
58 
57 
56 

6 

7 

54 

5-4 
6.3 

53 

5-3 

6.2 

5 
6 

8 
9 

9.38  620 
9.38  670 
9.38  721 
9.38  771 
9.38  821 

50 
5i 
5o 
50 

9-39  945 
9-39  999 
9.40  052 
9.40  106 
9.40  159 

54 
53 
54 
53 

0.60  055 
0.60  ooi 
0.59  948 
0.59  894 
0.59  841 

9.98  675 
9.98  671 
9.98  668 
9.98  665 
9.98  662 

4 

3 
3 
3 

55 
54 
53 
52 
5i 

8 
9 

10 

20 
30 

7-2 

8.1 
9.0 
18.0 
27.0 

7-1 
8.0 
8.8 
17.7 
26.5 

10 

ii 

12 
13 
14 

9-38  871 
9.38  921 
9.38  971 
9-39  02! 
9-39  071 

So 
50 
50 
50 

9.40  212 
9.40  266 
9.40  319 
9.40  372 
9.40  425 

54 
53 
53 
53 

0.59  788 

0-59  734 
0.59  681 
0.59  628 
o-59  575 

9.98  659 
9.98  656 
9.98  652 
9.98  649 
9  98  646 

3 
4 

3 
3 

50 

49 
48 
47 
46 

40 
50 

36.0 
45-o 

5« 

35-3 
44.2 

5i 

15 

16 

17 
18 

19 

9.39  121 
9-39  170 
9-39  220 
9.39  270 
9-39  319 

49 
50 
50 
49 

9.40  478 

9-40  531 
9.40  584 
9.40  636 
9.40  689 

53 
53 
52 
53 

0.59  522 
0.59  469 
0.59  416 
0-59  364 
0-59  3" 

9.98  643 
9.98  640 
9.98  636 
9-98  633 
9.98  630 

3 
4 
3 
3 

45 
44 
43 
42 
4i 

6 

7 
8 

9 

10 

5-2 

6.1 
6.9 
7.8 
8-7 

& 

6.8 

7-7 
8-5 

20 

21 
22 

23 
24 

9-39  369 
9-39  4i8 
9-39  467 
9-39  517 
9-39  566 

5° 
49 
49 
So 
49 

9.40  742 

9-40  795 
9.40  847 
9.40  900 
9.40  952 

53 
52 
53 
S2 

0.59  258 
0.59  205 

o-59  153 
0.59  100 
0.59  048 

9.98  627 
9.98  623 
9.98  620 
9.98  617 
9.98  614 

4 
3 
3 
3 

40 

39 
38 
37 
36 

20 
30 
40 

50 

17-3 
26.0 

34-7 
43-3 

17.0 

25-5 
34-o 
42-5 

25 
26 

27 
28 
29 

9-39  615 
9.39  664 

9-39  713 
9.39  762 
9-39  8n 

49 
49 
49 
49 

9.41  005 
9.41  057 
9.41  109 
9.41  161 
9.41  214 

52 
52 
52 
53 

o-58  995 
0-58  943 
0.58  891 
0.58  839 
0.58  786 

9.98  610 
9.98  607 
9.98  604 
9.98  601 
9  98  597 

3 
3 
3 
4 

35 
34 
33 
32 
3i 

•  6 
7 
8 

5° 

5-o 
5-8 
6-7 

49 
4-9 
5-7 
6-5 

30 

3i 
32 
33 
34 

9.39  860 
9.39  909 

9-39  958 
9.40  006 
9-40  055 

49 
49 
48 

49 
j.8 

9.41  266 
9.41  318 
9.41  370 
9.41  422 
9.41  474 

52 
52 
52 
52 

0-58  734 
0.58  682 
0.58  630 
0.58  578 
0.58  526 

9.98  594 
9.98  591 
9.98  588 
9-98  584 
9.98  581 

3 
3 
4 
3 

30 

29 
28 

27 
26 

9 

10 
20 

30 
40 

co 

7-5 
8-3 
16.7 
25.0 

33-3 
41.7 

7-4 

8.2 

16.3 

24-5 
32-7 
40  8 

!i 

37 
38 
39 

9.40  103 
9.40  152 

9.40  200 
9.40  249 
9.40  297 

49 
48 

49 

48 

9.41  526 
9-41  578 
9.41  629 
9.41  681 
9-41  733 

52 
5i 
S2 
52 

0.58  474 
0.58  422 
0.58  37i 
0.58  319 
0.58  267 

9.98  578 
9-98  574 
9.98  571 
9.98  568 
9.98  565 

4 
3 
3 
3 

25 
24 

23 

22 
21 

6 

48 
4.8 

C  fi 

47 

4-7 

c  •=•  • 

40 

4i 

42 
43 
44 

9.40  346 

9-40  394 
9.40  442 
9.40  490 
9-40  538 

48 
48 
48 
48 

A& 

9.41  784 
9.41  836 
9.41  887 

9-4i  939 
9.41  990 

52 
Si 
52 
5i 

0.58  216 
0.58  164 
0.58  113 
0.58  061 
0.58  oio 

9.98  561 
9-98  558 
9-98  555 
9-98  55i 
9.98  548 

3 
3 
4 
3 
3 

20 

19 

18 
17 
16 

7 
8 
9 

10 
20 

3° 

5-° 
6-4 
7.2 
8.0 
16.0 
24.0 

IS 

7-1 
7-8 
15-7 
23.5 

45 
46 

47 
48 

49 

9.40  586 
9.40  634 
9.40  682 
9.40  730 
9.40  778 

48 
48 
48 
48 

9.42  041 
9.42  093 
9.42  144 
9.42  195 
9.42  246 

52 
5i 
Si 
Si 

0-57  959 
0.57  907 
0.57  856 
0.57  805 
o.57  754 

9-98  545 
9.98  541 
9-98  538 
9-98  535 
9-98  53i 

4 
3 
3 
4 

15 
14 
13 

12 
.11 

40 
50 

32.0 
40.0 

4 

31-3 
39-2 

3 

50 

Si 
52 
53 
54 

9.40  825 
9.40  873 
9.40  921 
9.40  968 
9.41  016 

47 
48 
48 
47 
48 

9.42  297 
9.42  348 
9.42  399 
9.42  450 
9.42  501 

51 
5i 
5i 
5i 
5i 

0-57  703 
0.57  652 
0.57  601 
0-57  550 
o-57  499 

9.98  528 
9-98  525 
9.98  521 
9.98  518 
9-98  515 

3 
4 
3 
3 

10 

9 
8 
7 
6 

6 

8 
9 

10 

0.4 
o.5 
o.S 
0.6 
0.7 

0.3 
0.4 
0.4 

o.5 
o-S 

P 

57 
58 
59 

9.41  063 
9.4!  in 
9-41  158 
9.41  205 
9.41  252 

47 
48 
47 
47 
47 

9-42  552 
9.42  603 
9-42  653 
9.42  704 
9-42  75? 

51 
5* 
So 
51 
5* 

0.57  448 
0.57  397 
0-57  347 
0.57  296 
0-57  245 

9.98  511 
9.98  508 
9-98  505 
9-98  501 
9.98  498 

3 
3 
4 
3 

5 
4 
3 

2 

I 

20 

3° 
40 

50 

1-3 

2.0 
2.7 

3-3 

I.O 

i-5 

2.0 

2-5 

00 

9-41  300 

4° 

9-42  805 

5° 

0-57  195 

9.98  494 

0 

L.  Cos. 

d. 

L.  Cot£. 

c.  d. 

L.Taiii;. 

1,.  Sin. 

d. 

/ 

1'r 

op.  1 

•Is. 

75< 


37 


/• 

L.  Sin. 

d. 

L.Tang.  c.  d. 

L.  Cotg. 

JL.  Cos. 

d. 

Prop.  Pts. 

0 

I 

2 

3 
4 

9.41  300 
9-41  347 
9-41  394 
9.41  441 
9.41  488 

47 
47 
47 
47 
47 

47 
46 
47 
47 
46 

47 

46 

47 

46 

47 
46 
46 

47 
46 
46 
46 
46 
46 
46 
45 
46 
46 
46 
45 
46 

45 
46 
45 
46 
45 

45 
46 
45 
45 
45 
45 
45 
45 
45 
44 
45 
45 
45 
44 
45 
44 
45 
44 
45 
44 
44 
44 
45 
44 
44 

9.42  805 
9.42  856 
9.42  906 
9-42  957 
9.43  007 

51 

50 
51 
50 
5° 
51 
5° 
So 
So 
50 
So 
50 
So 
5° 
So 

49 
50 
50 
49 
50 

49 
50 
49 
So 
49 
49 
49 
So 
49 
49 
49 
49 
49 
49 
49 
48 
49 
49 
48 
49 

49 
48 

49 
48 
48 

49 
48 

48 
48 
49 
48 
48 
48 
48 
48 
48 
47 
48 
48 
48 

0-57  195 
0.57  144 
0.57  094 
0-57  043 
0-56  993 

9.98  494 
9.98  491 
9.98  488 
9.98  484 
9.98  481 

3 
3 
4 
3 
4 
3 
3 
4 
3 
4 
3 
4 
3 
3 
4 
3 
4 
3 
4 
3 
4 
3 
4 
3 
3 
4 
3 
4 
3 
4 
3 
4 
3 
4 
4 
3 
4 
3 
4 
3 
4 
3 
4 
3 
4 
4 
3 
4 
3 
4 
3 
4 
4 
3 
4 
3 
4 
4 
3 
4 

60 

59 
58 
57 
56 

6 

8 
9 

10 

20 

30 

40 

50 

6 

7 
8 

9 

10 
20 

3<> 
40 

5° 

6 

7 
8 

9 
10 

20 

30 
40 

50 

6 

7 
8 

9 

10 
20 

3° 

40 

50 

6 
7 
8 

9 

10 
20 

3° 

40 
50 

51 

5-1 
6.0 
6.8 
7-7 
8.5 
17.0 

25-5 
34-° 
42.5 

49 

4.9 
5-7 
6-5 
7-4 

8.2 

16.3 
24-5 
32-7 
40.8 

47 

4-7 
5-5 
6-3 
7-1 
7.8 
15-7 
23-5 
3i.3 
39-2 

45 

4-5 
5-3 
6.0 
6.8 

7-5 
15.0 
22.5 
30.0 
37-5 

4 

0.4 
o.S 
0-5 
0.6 
0.7 
i-3 

2.0 
2.7 

3-3 

50 

S-o 
5.8 
6.7 

7-5 
8-3 
16.7 
25.0 
33-3 
41.7 

48 
4.8 
5.6 
6.4 

7-2 

8.0 
16.0 
24.0 
32.0 
40.0 

46 

4.6 

5-4 
6.1 
6.9 
7-7 
15.3 
23.0 

30.7 
38.3 

44 

4.4 
5-i 
5-9 
6.6 

7-3 
14.7 

22.O 
29-3 

36.7 

3 

0-3 
0.4 
0.4 

o.S 

o.S 

I.O 

i-5 

2.0 

2-5 

t 

7 
8 

9 
1O 

ii 

12 

13 
14 

9-4i  535 
9.41  582 
9.41  628 
9-4i  675 
9.41  722 

9-43  057 
9-43  i°8 
9-43  158 
9-43  208 
9-43  258 

0.56  943 
0.56  892 
0.56  842 
0.56  792 
0.56  742 

9.98  477 
9.98  474 
9.98  471 
9.98  467 
9.98  464 

55 
54 
53 

52 
5i 

9.41  768 
9.41  815 
9.41  861 
9.41  908 
9-4i  954 

9-43  3°8 
9  43  358 
9-43  408 
9.43  458 
9  43  5o8 

0.56  692 
0.56  642 
0.56  592 
0.56  542 
0.56  492 

9.98  460 
9-98  457 
9-98  453 
9.98  450 
9.98  447 

50 

49 
48 

47 
46 

IS 

16 

17 
18 

19 

9.42  ooi 
9.42  047 
9.42  093 
9.42  140 
9.42  186 

9-43  558 
9  43  607 
9-43  657 
9-43  707 
9-43  756 

0.56-442 
0-56  393 
0-56  343 
0.56  293 
0.56  244 

9.98  443 
9.98  440 
9.98  436 
9-98  433 
9  98  429 

45 
44 
43 
42 

41 

20 

21 
22 
23 

24 

9.42  232 
9.42  278 
9.42  324 
9.42  370 
9.42  416 

9-43  806 
9-43  855 
9-43  9°5 
9-43  954 
9.44  004 

0.56  194 
0.56  145 
0.56  095 
0.56  046 
0-55  996 

9.98  426 
9.98  422 
9.98  419 
9.98  415 
9.98  412 

40 

39 
38 
37 
36 

25 
26 

27 
28 
29 

9.42  461 
9.42  507 
9-42  553 
9.42  599 
9-42  644 

9-44  °53 
9.44  102 

9-44  I5i 
9.44  201 
9-44  250 

o-55  947 
0.55  898 
0-55  849 
o.55  799 
0-55  750 

9.98  409 
9.98  405 
9.98  402 
9.98  398 
9-98  395 

35 
34 
33 
32 
3i 

30 

3i 
32 
33 
34 

9.42  690 
9-42  735 
9.42  781 
9.42  826 
9.42  872 

9-44  299 
9.44  348 

9-44  397 
9.44446 
9-44  495 

0-55  70i 
0-55  652 
0.55  603 
o-SS  554 
o-55  5°5 

9.98  391 
9.98  388 
9.98  384 
9.98  381 
9-98  377 

3O 

29 
28 

27 
26 

35 
36 
37 
38 
39 

9.42  917 
9.42  962 
9-43  °°8 
9-43  °53 
9-43  098 

9-44  544 
9.44  592 

9-44  641 
9.44  690 
9-44  738 

0-55  456 
0.55  408 

0-55  359 
0-55  3io 
0.55  262 

9-98  373 
9.98  370 
9.98  366 
9-98  363 
9-98  359 

25 
24 

23 

22 
21 

40 

4i 

42 
43 
44 

9-43  143 
9-43  188 
9-43  233 
9-43  278 
9-43  323 

9-44  787 
9-44  836 
9-44  884 
9-44  933 
9.44981 

o-55  213 
0.55  164 
0.55  116 
0.55  067 
0.55  019 

9-98  356 
9  98  352 
9-98  349 
9-98  345 
9.98  342 

20 

19 

18 

17 
16 

45 
46 

47 
48 
49 

9-43  367 
9-43  412 
9-43  457 
9-43  502 
9-43  546 

9.45  029 
9-45  078 
9.45  126 

9-45  174 
9-45  222 

0.54  971 
0.54  922 
0.54  874 
0.54  826 
0-54  778. 

9.98  338 
9-98  334 
9-98  33i 
9.98  327 
9.98  324 

15 
14 
13 

12 
II 

5O 

Si 
52 
53 
54 

9-43  59i 
9-43  635 
9.43  680 

9-43  724 
9-43  769 

9.45  271 
9-45  319 
9-45  367 
9-45  415 
9-45  463 

0.54  729 
0.54  681 
0.54  633 
0-54  585 
°-54  537 

9.98  320 
9.98  317 
9-98  313 
9.98  309 
9.98  306 

10 

'9 

8 

7 
6 

55 
56 
57 
58 
59 

9-43  813 
9-43  857 
9-43  901 
9.43  946 

9-43  990 

9-45  5ii 
9-45  559 
9-45  606 
9-45  654 
9-45  7°2 

0.54  489 
0.54  441 
°-54  394 
o-54  346 
0.54  298 

9.98  302 
9.98  299 
9.98  295 
9.98  291 
9.98  288 

5 
4 
3 

2 

I 

60 

9.44  034 

9-45  750 

0.54  250 

9.98  284 

o 

L.  Cos. 

d. 

L.Cotg. 

c,  d.JL.Tang. 

L.  Sin. 

d. 

r 

Prop.  Pts. 

74< 


16' 


/• 

L.  Sin. 

d. 

L.Tang.  c.  d.  L.  Cotg. 

L.  Cos.   d. 

Prop.  Pts. 

o 

I 

2 

3 
4 

9-44  034 
9-44  078 
9.44  122 
9.44  166 
9.44  210 

44 
44 
44 
44 
43 
44 
44 
44 
43 
44 
44 
43 
43 
44 
43 
44 
43 
43 
43 
43 
43 
44 
43 
42 

43' 
43 
43 
43 
43 
42 

43 
42 
43 
42 

43 
42 
43 
42 
42 
42 
43 
42 
42 
42 
42 
42 
42 
42 
4i 
42 
42 
42 
41 
42 
4i 
42 
4i 
42 
4» 
42 

9-45  750 
9-45  797 
9-45  845 
9-45  892 
9-45  940 

47 
48 
47 
48 

47 
48 
47 
48 
47 
47 
47 
48 
47 
47 
47 
47 
47 
47 
47 
46 

47 
47 
47 
46 
47 

47 
46 

47 
46 
46 

47 
46 
46 
47 
46 

46 
46 
46 
46 
46 
46 
46 
46 
46 
46 

45 
46 

46 
46 
45 
46 
45 
46 
45 
45 
46 
45 
45 
46 
45 

0-54  250 
0.54  203 

0-54  155 
0.54  108 
0.54  060 

9.98  284 
9.98  281 
9.98  277 
9.98  273 
9.98  270 

3 
4 
4 
3 
4 
4 
3 
4 
4 
3 
4 
4 
3 
4 
4 
3 
4 
4 
3 
4 
4 
3 
4 
4 
4 
3 
4 
4 
4 
3 
4 
4 
4 
3 
4 
4 
4 
3 
4 
4 
4 
3 
4 
4 
4 
4 
3 
4 
4 
4 
4 
4 
3 
4 
4 
4 
4 
4 
4 

00 

59 
58 
57 
56 

6 
7 
8 

9 

10 
20 
30 
40 
50 

6 

7 
8 
9 

10 

20 
30 
40 
50 

6 

7 
8 

9 

10 
20 

3° 

40 
50 

6 

7 
8 

9 

10 
20 
30 
40 

50 

6 

7 
8 
9 

10 
20 
30 
40 

50 

48 

4.8 
5-6 
6-4 
7.2 
8.0 
16.0 
24.0 
32.0 
40.0 

46 

4.6 

5-4 
6.1 

6-9 
7-7 
15-3 
23.0 

3°-7 
38-3 

44 

4-4 
5-1 
5-9 
6.6 

7-3 
147 

22.0 

29-3 
36.7 

43 

4-2 

4-9 
5-6 
6-3 
7-o 
14.0 

21.0 
28.0 

35-0 

4 
0.4 
0-5 
0.5 
0.6 
0.7 
i-3 

2.0 
2.7 

3-3 

47 

4-7 

il 

7.1 

7-8 
15-7 
23-5 
31-3 
39-2 

45 

4-5  . 
5-3 
6.0 
6.8 
7-5 
15-0 
22.5 
30.0 
37-5 

43 

4-3 
5-0 
5-7 
6-5 

7-2 

14-3 
21-5 
28.7 
35-8 

4i 
4.1 
4-8 

I:! 

6.8 
13-7 
20.5 

27-3 
34-2 

3 

0-3 
0.4 
0.4 
0-5 
0-5 

I.O 

i-5 

2.0 
2-5 

5 
6 

7 
8 

9 

9-44  253 
9-44  297 
9-44  34i 
9  44  385 
9-44  428 

9-45  987 
9-46  035 
9.46  082 
9.46  130 
9.46  177 

0.54  013 
o-53  965 
0-53  9i8 
0.53  870 
0.53  823 

9.98  266 
9.98  262 
9  98  259 
9-98  255 
9.98  251 

55 
54 
53 
52 
5i 

10 

ii 

12 

13 
14 

9.44  472 
9-44  5i6 
9-44  559 
9.44  602 
9-44  646 

9.46  224 
9.46  271 
9.46  319 
9.46  366 
9.46  413 

o.53  776 
0-53  729 
0.53  681 

0-53  634 
0.53  587 

9.98  248 
9.98  244 
9.98  240 
9.98  237 
9-98  233 

50 

49 
48 

47 
46 

15 

16 

17 

18 

19 

9.44  689 

9-44  733 
9.44  776 

9-44  819 
9.44  862 

9.46  460 
9.46  507 

9-46  554 
9.46  601 
9.46  648 

0-53  540 
0-53  493 
0-53  446 
0-53  399 
o.53  352 

9.98  229 
9.98  226 

9.98  222 

9.98  218 

9.98  215 

45 
44 
43 
42 
41 

20 

21 
22 
23 
24 

9-44  9°5 
9-44  948 
9-44  992 
9-45  035 
9-45  077 

9.46  694 
9.46  741 
9.46  788 
9-46  835 
9.46  881 

0.53  306 
o.53  259 

0.53  212 
0-53  165 

0.53  "9 

9.98  211 
9.98  207 
9.98  204 
9.98  2OO 
9.98  196 

40 

39 
38 

H 

25 
26 
27 
28 
29 

9-45  120 
9-45  163 
9-45  206 
9-45  249 
9.45  292 

9.46  928 
9.46  975 
9.47  021 
9.47  068 
9-47  "4 

0.53  072 

0.53  025 
0.52  979 
0.52  932 
0.52  886 

9.98  192 
9.98  189 
9.98  I8f 

9.98  181 
9.98  177 

35 
34 
33 
32 
3i 

3O 

3i 

32 
33 
34 

9-45  334 
9-45  377 
9-45  419 
9-45  4°2 
9-45  504 

9.47  160 
9.47  207 
9-47  253 
9-47  299 
9-47  346 

0.52  840 
0.52  793 
.0.52  747 
0.52  701 
0.52  654 

9.98  174 
9.98  170 
9.98  166 
9.98  162 
9.98  159 

30 

29 
28 
27 
26 

35 
36 
37 
38 
39 

9-45  547 
9-45  589 
9-45  632 
9-45  674 
9-45  7i6 

9-47  392 
9-47  438 
9.47  484 
9-47  530 
9-47  576 

0.52  608 
0.52  562 
0.52  516 
0.52  470 
0.52  424 

9-98  155 
9.98  151 
9.98  147 
9.98  144 
9.98  140 

25 
24 
23 

22 
21 

40 

4i 
42 

43 
44 

9-45  758 
9-45  801 
9-45  843 
9-45  885 
9-45  927 

9.47  622 
9.47  668 
9-47  7H 
9-47  760 
9.47  806 

0.52  378 
0.52  332 
0.52  286 
0.52  240 
0.52  194 

9.98  136 
9.98  132 
9.98  129 
9-98  125 

9.98  121 

20 

19 
18 

17 
16 

45 
46 

47 
48 
49 

9-45  969 
9.46  on 

9-46  °53 
9.46  095 
9.46  136 

9-47  852 
9-47  897 
9-47  943 
9-47  989 
9-48  035 

0.52  148 
0.52  103 
0.52  057 
0.52  on 
9-Si  965 
0.51  920 
0.51  874 
0.51  829 
0.51  783 
0.51  738 

9.98  117 
9.98  II3 

9.98  no 
9.98  106 
9.98  102 

15 
14 
13 

12 

11 

50 

Si 
52 
53 
54 

9.46  178 
9.46  220 
9.46  262 
9-46  303 
9-46  345 

9.48  080 
9.48  126 
9.48  171 
9.48  217 
9.48  262 

9.98  098 
9.98  094 
9.98  090 
9.98  087 
9-98  083 

10 

9 

8 

7 
6 

55 
56 
57 
58 
59 

9-46  386 
9.46  428 
9.46  469 
9.46  511 
9-46  552 

9.48  307 
9-48  353 
9.48  398 
9-48  443 
9.48  489 

0.51  693 
0.51  647 
0.51  602 
0-51  557 
0.51  5" 

9.98  079 
9.98  075 
9.98  071 
9.98  067 
9-98  063 

5 
4 
3 

a 

00 

9-46  594 

9-48  534 

0.51  466 

9.98  060 

0 

L.  Cos.  |  d. 

L.  Cotg.  C.  d.  L.TMIIU. 

L.  Sin.   d. 

/ 

Prop.  Pts. 

73C 


17' 


39 


/- 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

Prop.  Pts. 

o 

I 

2 

3 
4 

9.46  594 
9-46  635 
9.46  676 
9.46  717 
9.46  758 

41 
41 
41 
41 
42 

41 
41 
41 
41 
41 
40 
41 
41 
41 
41 
40 
41 
40 
41 
40 

41 
40 

41 
40 
40 

41 
40 
40 
40 
40 
40 
40 
40 
40 
40 
40 
40 

39 
40 
40 

39 
40 
40 
39 

9-48  534 
9-48  579 
9.48  624 
9.48  669 
9.48  714 

45 
45 
45 
45 
45 
45 
45 
45 
45 
45 
45 
44 
45 
45 
44 
45 
44 
45 
44 
45 
44 
45 
44 
44 
45 
44 
44 
44 
44 
44 
44 
44 
44 
44 
44 
44 
44 
43 
44 
44 
44 
43 
44 
43 
44 
43 
44 
43 
44 
43 
43 
44 
43 
43 
43 
43 
43 
44 
43 
43 

0.51  466 
0.51  421 
0.51  376 

0-51  33i 
0.51  286 

9.98  060 
9.98  056 
9.98  052 
9.98  048 
9.98  044 

4 
4 
4 
4 
4 
4 
4 
3 
4 
4 
4 
4 

4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 
4 

6O 

59 

58 

fa 

6 

7 
8 

9 

10 
20 

3° 

4 
$ 
5 
6 
6 
1 
15 

25 

3^ 

37 

6 

7 
8 

9 
10 

20 
30 
40 
50 

4 

4 
A 

5 
6 

7 

14 

21 

28 

35 

4 

4 

4 

6 
6 
13 

20 
26 

33 
5 

5-5 

).6 

)-7 
).8 
).8 
•7 

»-s 

i-3 

\.2 

5 

•5 
•3 

.0 

.8 

•5 

.0 

•5 

.0 

•  5 

4 

4 

c 
1 

( 

7 

M 

23 
2£ 

3  = 
* 

.2 

•9 

.6 

•3 
.0 
.0 

.0 
.0 
.0 

0 

.0 

•7 
•3 
.0 

•7 

•3 

.0 

•7 
•3 

4 
o. 

0. 

o. 
o 

0. 

I. 

2. 
2. 

3- 

44 

4.4 
S-i 

5.9 

6.6 
7-3 
14-7 

22.0 
29-3 
36.7 

3 

k3 

.0 

•7 
•5 

.2 

\-3 
•5 
.7 
.8 

4i 

4.1 
4.8 
5-5 

6.2 

6.8 

13-7 
20.5 

27-3 
34-2 

39 

3-9 
4.6 

5-2 

5-9 
6-5 
13.0 

19.5 
26.0 

32-5 

3 
4    0.3 
5    0.4 
5    0.4 
6    0.5 
7    0.5 
3    i-o 
o    1.5 
7    2.0 
3    2.5 

6 

7 
8 

9 

9.46  800 
9.46  841 
9.46  882 
9.46  923 
9.46  964 

9-48  759 
9.48  804 
9.48  849 
9.48  894 
9.48  939 

0.51  241 
0.51  196 
0.51  151 
0.51  106 
0.51  061 

9.98  040 
9.98  036 
9.98  032 
9.98  029 
9.98  025 

55 
54 
53 
52 
5i 

10 

ii 

12 
13 
14 

9.47  005 
9-47  045 
9.47  086 
9-47  127 
9.47  168 

9.48  984 
9.49  029 

9-49  073 
9.49  118 
9-49  163 

0.51  016 
0.50  971 
0.50  927 
0.50  882 
0.50  837 

9.98  021 

9  98  017 
9  98  013 
9.98  009 
9.98  005 

50 

49 
48 

47 
46 

40 
50 

15 

16 

17 
18 

19 

9-47  209 
9-47  249 
9-47  290 
9-47  330 
9-47  37i 

9-49  207 
9-49  252 
9.49  296 
9-49  341 
9-49  385 

0.50  793 
0.50  748 
0.50  704 
0.50  659 
0.50  615 

9.98  ooi 
9-97  997 
9-97  993 
9  97  989 
9-97  986 

45 
44 
43 
42 

4i 

20 

21 
22 

23 

24 

9.47411 
9  47  452 
9.47  492 
9-47  533 
9-47  573 

9-49  430 
9.49  474 

9-49  519 
9-49  563 
9.49  607 

0.50  570 
0.50  526 
0.50  481 
0.50  437 
0.50  393 

9-97  982 
9.97  978 
9-97  974 
9-97  970 
9-97  966 

40 

39 
38 
37 
36 

6 

7 
8 

25 
26 

27 

28 
29 

9.47  613 
9-47  654 
9-47  694 
9-47  734 
9-47  774 

9.49  652 
9-49  696 
9.49  740 
9.49  784 
9.49  828 

0.50  348 
0.50  304 
0.50  260 
0.50  216 
0.50  172 

9-97  962 
9-97  958 
9-97  954 
9-97  950 
9-97  946 

35 
34 
33 
32 
3i 

3O 

3i 
32 
33 
34 

9.47  814 

9-47  854 
9.47  894 

9-47  934 
9.47  974 

9  49  872 
9.49  916 
9.49  960 
9.50  004 
9.50  048 

0.50  128 
0.50  084 
0.50  040 
0.49  996 
0.49  952 

9.97  942 
9-97  938 
9-97  934 
9-97  930 
9-97  926 

3O 

29 
28 
27 
26 

9 
10 

20 
30 
40 
50 

6 

7 
8 

9 

10 

20 
30 
40 
50 

6    c 

7    < 
8    c 

9    < 

10     C 
20      1 

30      '. 

40  : 

50  t 

35 
36 
37 
38 
39 

9.48  014 
9.48  054 
9.48  094 
9-48  133 
9.48  173 

9.50  092 
9.50  136 
9.50  180 
9.50  223 
9.50  267 

0.49  908 
0.49  864 
o  49  820 
0.49  777 
0-49  733 

9.97  922 
9-97  9i8 
9.97  914 

9-97  910 
9.97  906 

25 
24 
23 

22 
21 

40 

4i 

42 

43 
44 

9.48  213 
9.48  252 
9.48  292 
9-48  332 
9-48  37i 

9-503II 
9  So  355 
9-50  398 
9.50  442 

9-5°  485 

0.49  689 
0.49  645 
0.49  602 
0-49  558 
049515 

9-97  902 
9.97  898 
9-97  894 
9-97  890 
9.97  886 

20 

19 
18 
17 
16 

45 
46 

47 
48 
49 

9.48  411 
9.48  450 
9.48  490 
9.48  529 
9.48  568 

40 

39 
40 

39 
39 

9-5°  529 
9-So  572 
9.50  616 
9-50  659 
9-50  7°3 

0.49  471 
0.49  428 
0.49  384 

0-49  34i 
0.49  297 

9.97  882 
9-97  878 
9-97  874 
9-97  870 
9.97  866 

15 
14 
13 

12 
II 

5O 

Si 
52 
53 

54 

9.48  607 
9.48  647 
9.48  686 
9.48  725 
9.48  764 

39 
40 
39 
39 
39 

9.50  746 
9.50  789 
9-50  833 
9.50  876 
9.50919 

0.49  254 

0.49  211 
0.49  167 
0.49   124 
0.49  08  1 

9.97  861 
9-97  857 
9-97  853 
9-97  849 
9-97  845 

4 

10 

9 

8 

7 
6 

55 
56 
57 
58 
59 

9.48  803 
9.48  842 
9.48  881 
9.48  920 
9.48  959 

39 
39 
39 
39 
39 
39 

9.50  962 
9.51  005 
9.51  048 
9.51  092 
9-51  135 

0.49  038 

0.48  995 
0.48  952 
0.48  908 
0.48  865 

9.97  841 
9-97  837 
9-97  833 
9-97  829 
9.97  825 

4 
4 
4 
4 
4 

5 
4 
3 

2 

I 

60 

9.48  998 

9.51  178 

0.48  822 

9.97  821 

O 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.Tang. 

L.  Sin. 

d. 

r 

Prop.  Pts. 

72< 


r 

!  .  Sill. 

d. 

L.Taiig. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

Pi 

01 

>. 

Pts. 

O 

i 

2 

3 
4 

9.48  998 

9-49  °37 

9.49  076 

9-49  US 
9-49  153 

39 
39 
39 
38 

9.51  178 

9.51   221 
9-51  264 
9.51  306 

9-51  349 

43 
43 
42 
43 

0.48  822 
0.48  779 
0.48  736 
0.48  694 
0.48  651 

9.97  821 
9-97  817 
9.97  812 
9.97  808 
9-97  804 

4 
5 

4 
4 

60 

59 
58 
57 
56 

6 
7 

4 

4 
5 

3 
•3 

.0 

4» 

4-2 

4-9 

5 
6 
7 
8 
9 

9-49  192 
9-49  231 
9-49  269 
9-49  3o8 
9-49  347 

39 
38 
39 
39 
•38 

9-5i  392 
9-5i  435 
9.51  478 
9-5i  520 
9-5i  563 

43 
43 
43 
42 
43 

0.48  608 
0.48  565 
0.48  522 
0.48  480 
0.48  437 

9.97  800 
9-97  796 
9-97  792 
9.97  788 
9-97  784 

4 

4 
4 
4 

55 
54 
53 
52 
5i 

8 
9 

10 
20 
30 

\ 

7 
M 

21 

-7 
•5 

.2 

•3 

•5 

5-6 
6-3 
7.0 
14.0 

2C.O 

10 

ii 

12 
13 
14 

9-49  385 
9-49  424 
9-49  462 
9-49  5oo 
9-49  539 

39 
38 
38 
39 

-0 

9.51  606 
9.51  648 
9.51  691 

9-5i  734 
9.51  776 

43 
42 
43 
43 
42 

0.48  394 
0.48  352 
0.48  309 
0.48  266 
0.48  224 

9-97  779 
9-97  775 
9-97  771 
9-97  767 
9-97  763 

4 
4 

4 
4 

50 

49 
48 
47 
46 

40 
50 

2b 

35 

•7 

.8 

4 

28.0 

35-0 

i 

15 

16 

17 
18 

19 

9-49  577 
9-49  615 
9.49  654 
9.49  692 
9-49  730 

38 

39 
38 
38 

_Q 

9.51  819 
9.51  861 

9-5i  903 
9.51  946 
9.51  988 

43 
42 
42 

43 
42 

0.48  181 
0.48  139 
0.48  097 
0.48  054 

0.48  012 

9-97  759 
9-97  754 
9-97  75° 
9-97  746 
9-97  742 

5 
4 
4 
4 

45 
44 
43 
42 
4i 

6 

7 
8 

9 

10 

t 

A 
c 

I 

t 

kl 

ki 
•s 

).2 

.8 

20 

21 
22 
23 
24 

9-49  768 
9.49  806 

9-49  844 
9.49  882 
9.49  920 

38 
38 
38 
38 

9.52  031 
9-52  073 
9-52  115 
9-52  157 

9.52  200 

43 
42 
42 
42 
43 

0.47  969 
0.47  927 
0.47  885 
0.47  843 
0.47  800 

9-97  738 
9-97  734 
9.97  729 
9-97  725 
9-97  721 

4 

5 
4 
4 

40 

39 
38 
37 
36 

20 
30 
P 
>0 

\.-. 

2C 

^ 

3-1 

•7 

'•5 
•3 

^•2 

5 

27 
28 

29 

9-49  958 
9-49  996 
9-5°  034 
9.50  072 
9.50  no 

38 
38 
38 
38 
38 

9.52  242 
9.52  284 
9.52  326 
9.52  368 
9.52  4IO 

42 
42 
42 
42 
42 

0.47  758 
0.47  7l6 
0.47  674 

0.47  632 
0.47  590 

9-97  717 
9-97  713 
9-97  708 
9-97  704 
9-97  700 

4 
5 
4 
4 

35 
34 
33 
32 
3i 

.  6 

7 
8 

3 

3 
4 
5 

9 

•9 
.6 

.2 

38 

3-8 
4-4 
5-i 

3O 

3i 

32 
33 
34 

9.50  148 
9-50  185 
9.50  223 
9.50  261 
9.50  298 

3° 
37 
38 
38 
37 

9-52  452 

9-52  494 
9-52  536 
9-52  578 
9.52  620 

42 
42 
42 
42 
42 

0.47  548 
0.47  506 
0.47  464 
0.47  422 
0.47  380 

9-97  696 
9.97  691 
9-97  687 
9  97  683 
9-97  679 

5 
4 
4 
4 

30 

29 
28 
27 
26 

9 

10 
20 

30 
40 

CQ 

i 
6 

13 
19 
at 

•9 

•5 

.0 

•5 
.0 

5-7 
6-3 
12.7 
19.0 
25-3 

35 
36 
37 
38 
39 

9-50  336 
9-5°  374 
9.50  411 

9-50  449 
9.50  486 

S8 

38 
37 
38 
37 

9.52  661 
9-52  703 
9-52  745 
9.52  787 
9.52  829 

41 
42 
42 
42 
42 

0-47  339 
0.47  297 
0-47  255 
0.47  213 
0.47  171 

9-97  674 
9-97  670 
9.97  666 
9.97  662 
9-97  657 

5 
4 
4 
4 
5 

25 
24 
23 

22 
21 

6 

3 
3 

7 
•7 

36 
3-6 

40 

4i 
42 

43 

44 

9-5°  523 
9.50  561 
9-50  598 
9-50  635 
9-50  673 

37 
38 
37 
37 
38 

9.52  870 
9.52  912  . 
9-52  953 
9-52  995 
9-53  °37 

41 
42 
4» 
42 
42 

0.47  130 
0.47  088 
0.47  047 
0.47  005 
0.46  963 

9-97  653 
9-97  649 
9-97  645 
9.97  640 
9-97  636 

4 
4 
5 
4 

2O 

19 

18 
17 
16 

7 
8 

9 

10 

20 
3° 

4 
4 

I 

12 

Ifi 

•3 
•9 

.6 

.2 

•3 

c 

4.2 
4.8 

5-4 
6.0 

12.0 

18.0 

45 
46 
47 
48 
49 

9.50  710 
9-5°  747 
9.50  784 
9.50  821 
9.50  858 

37 
37 
37 
37 
37 

9-53  078 
9-53  120 
9-53  161 
9-53  202 
9-53  244 

41 
42 
4i 
4» 
42 

0.46  922 
0.46  880 
0.46  839 
0.46  798 
0.46  756 

9-97  632 
9.97  628 
9  97  623 
9.97  619 
9-97  615 

4 
5 
4 
4 

15 
14 
13 

12 
II 

40 

50 

24 
30 

.7 

.8 

24.0 
30.0 

50 

Si 
52 
53 
54 

9.50  896 

9-5°  933 
9.50  970 
9.51  007 
9-Si  043 

38 
37 
37 
37 
36 

9-53  285 
9-53  327 
9-53  368 
9-53  409 
9-53  450 

4X 
42 
4* 
4* 

4i 

0.46  715 
0.46  673 
0.46  632 
0.46  591 
0.46  550 

9.97  610 
9.97  606 
9.97  602 
9-97  597 
9-97  593 

4 
4 
5 

4 

10 

9 
8 

7 
6 

6 

7 
8 

9 
10 

0 

o 

0° 

0 

S 
•7 
.8 

s 

0.4 
0-5 
0-5 
0.6 
0.7 

H 

57 
58 
59 

9.51  080 
9-Si  "7 
9-Si  154 
9.51  191 
9-Si  227 

37 
37 
37 
37 
36 

9-53  492 
9-53  533 
9-53  574 
9-53  6i5 
9-53  656 

42 

4i 
4' 
4i 
4» 

0.46  508 
0.46  467 
0.46  426 
0.46  385 
0.46  344 

9-97  589 
9-97  584 
9-97  58o 
9-97  576 
9-97  571 

5 

4 
4 
5 

5 
4 
3 

2 

20 
30 
40 
50 

J 

2 
4 

•7 

s 

3 

i 

1-3 

2.0 
2-7 
3-3 

00 

9.51  264 

37 

9-53  697 

41 

0.46  303 

9-97  567 

o 

L.  Cos. 

d. 

L.  Cotg. 

C.  d. 

L.Tang. 

L.  Sin. 

d. 

r 

Tr 

<M 

.  1 

Ms. 

71° 


19C 


r 

L.  Sin. 

d. 

L.Tang. 

c.  d. 

L.Cotg. 

L.  Cos. 

d. 

Pr 

op. 

Pts. 

0 

i 

2 

3 
4 

9.51  264 
9-Si  301 
9-5i  338 
9-Si  374 
9-51  4" 

37 
37 
36 
37 
ofi 

9-53  697 
9-53  738 
9-53  779 
9-53  820 
9-53  861 

41 
41 
4i 
4* 

0.46  303 
0.46  262 

0.46  221 

0.46  180 
0.46  139 

9-97  567 
9-97  563 
9-97  558 
9-97  554 
9-97  550 

4 
5 
4 
4 

GO 

59 
58 
57 
56 

6 
7 

41 
4.1 

4.8 

40 

4.0 

4-7 

6 

7 
8 

9 

9-Si  447 
9.51  484 
9-51  520 
9-5i  557 
9-5i  593 

3° 
37 
36 
37 
36 
ifi 

9-53  902 
9-53  943 
9-53  984 
9-54  025 
9-54  065 

4i 
41 

4i 
40 

0.46  098 
0.46  057 
0.46  016 
o.45  975 
0-45  935 

9-97  545 
9-97  541 
9-97  536 
9-97  532 
9.97  528 

4 
5 
4 
4 

55 
54 
53 
52 
Si 

8 
9 

10 

20 
30 

5-5 

6.2 

6.8 

13-7 

20.5 

5-3 
6.0 

6-7 
13-3 

2O.O 

10 

ii 

12 
13 

14 

9.51  629 
9.51  666 
9.51  702 
9-51  738 
9-5i  774 

3° 
37 
36 
36 
36 

9.54  106 
9-54  147 
9-54  187 
9-54  228 
9-54  269 

4i 
40 

4i 

41 

0.45  894 

0-45  853 
0.45  813 
0.45  772 
o-45  73i 

9-97  523 
9-97  519 
9-97  515 
9-97  5io 
9.97  506 

4 
4 
5 
4 

50 

49 

48 

47 
46 

40 

50 

27.3 
34-2 

3 

26.7 

33-3 

9 

15 

16 
17 
18 
19 

9-51  811 
9.51  847 
9-51  883 
9.51  919 

9-Si  955 

37 
36 
36 
36 
36 

9-54  3°9 
9-54  350 
9-54  390 
9-54  43i 
9-54  47i 

4° 

4i 

40 

4i 
40 

0.45  691 
0.45  650 
0.45  610 
o-45  569 
o-45  529 

9-97  501 
9-97  497 
9-97  492 
9.97  488 
9.97  484 

4 
5 
4 
4 

45 
44 
43 
42 
4i 

] 

6      3 
7      4 
8      5 
9      5 
:o      6 

•9 
.6 

.2 

•9 

•5 

20 

21 
22 

23 
24 

9-Si  99i 
9.52  027 
9.52  063 
9.52  099 
9-52  135 

3° 

36 
36 
36 
36 
ifi 

9-54  512 
9-54  552 
9-54  593 
9-54  633 
9-54  673 

41 
40 
41 
40 
40 

0.45  488 
0.45  448 
0.45  407 
o-45  367 
o-45  327 

9-97  479 
9-97  475 
9.97  470 
9.97  466 
9-97  461 

4 
5 
4 
5 

40 

39 
38 
37 

36 

t 
i 

to    13 
jo    15 

[0     26 

;o  32 

.0 

•5 

.0 

•5 

25 
26 
27 
28 
29 

9.52  171 
9.52  207 
9.52  242 
9-52  278 
9-52  3H 

3° 
36 
35 
36 
.36 
•36 

9-54  714 
9-54  754 
9-54  794 
9-54  835 
9-54  875 

40 
40 
41 
40 

0,45  286 
0.45  246 
0.45  206 
0.45  165 
0-45  125 

9-97  457 
9-97  453 
9.97  448 
9.97  444 
9-97  439 

4 

5 
4 
5 

35 
34 
33 
32 
3i 

6 

7 
8 

37 

3-7 
4-3 
4-9 

36 

3-6 

4-2 

4.8 

3O 

3i 
32 

33 
34 

9-52  350 
9-52  385 
9-52  421 
9-52  456 
9.52  492 

3° 

35 
36 
35 
36  . 

9-54  915 
9-54  955 
9-54  995 
9-55  035 
9-55  °75 

4° 
40 
40 
40 
40 

0.45  085 

0-45  045 
0.45  005 
0.44  965 
0.44  925 

9-97  435 
9-97  430 
9.97  426 
9.97  421 
9-97  417 

5 
4 
5 
4 

30 

29 
28 

27 
26 

9 
10 

20 

3° 
40 

CQ 

5-o 

6.2 

12.3 

18.5 
24.7 

qo  8 

5-4 
6.0 

12.0 

18.0 
24.0 

qo  O 

35 
36 
37 
38 
39 

9-52  527 
9-52  563 
9-52  598 
9-52  634 
9.52  669 

35 
36 
35 
36 
35 

9-55  H5 
9-55  155 
9-55  195 
9-55  235 
9-55  275 

40 
40 
40 

4° 
40 

0.44  885 
0.44  845 
0.44  805 
0.44  765 
0.44  725 

9-97  412 
9-97  4°8 
9-97  403 
9-97  399 
9-97  394 

4 
5 
4 
5 

25 
24 
23 

22 
21 

6 

35 

3-5 

34 

3-4 

40 

4i 
42 

43 
44 

9-52  705 
9.52  740 
9-52  775 
9.52  811 
9-52  846 

3° 
35 
35 
36 
35 

9-55  315 
9-55  355 
9-55  395 
9-55  434 
9-55  474 

4° 
40 
40 

39 
40 

0.44  685 
o.44  645 
0.44  605 
0.44  566 
0.44  526 

9-97  39° 
9-97  385 
9-97  38i 
9-97  376 
9-97  372 

5 
4 
5 
4 

20 

19 
18 

17 
16 

7 
8 

9 
10 
20 
30 

4.1 
4-7 
5-3 
5-8 
11.7 
17.5 

4.0 
4-5 
S-i 
5-7 
".3 
17.0 

45 
46 

47 
48 
49 

9.52  881 
9.52  916 
9-52  95i 
9.52  986 
9-53  021 

35 
35 
35 
35 
35 

9-55  5H 
9-55  554 
9-55  593 
9-55  633 
9-55  673 

40 
40 

39 
40 
40 

0.44  486 
0.44  446 
0.44  407 
0.44  367 
0.44  327 

9-97  367 
9-97  363 
9-97  358 
9-97  353 
9-97  349 

4 

5 
5 
4 

15 
14 
13 

12 
II 

40 
So 

23-3 
29.2 

22.7 
28.3 

5O 

Si 
52 
53 
54 

9-53  056 
9-53  092 
9-53  126 
9-53  161 
9-53  196 

35 
36 
34 
35 

35 

9-55  712 
9-55  752 
9-55  791 
9-55  831 
9-55  870 

39 
40 

39 
40 
39 

0.44  288 
0.44  248 
0.44  209 
0.44  169 
0.44  130 

9-97  344 
9-97  340 
9-97  335 
9-97  331 
9-97  326 

4 
5 
4 
5 

10 

9 
8 

7 
6 

6 

7 
8 

9 

10 

o.5 
0.6 
0.7 
0.8 

08 

0.4 
o-5 
o-5 
0.6 
0.7 

55 
56 
57 
58 
59 

9-53  231 
9-53  a66 
9-53  301 
9-53  336 
9-53  370 

35 
35 
35 
35 
34 

9-55  9Jo 
9-55  949 
9-55  989 
9.56  028 
9.56  067 

40 

39 
4° 
39 
39 

0.44  090 
0.44  051 
0.44  on 

0.43  972 

0-43  933 

9-97  322 
9-97  317 
9  97  312 
9-97  308 
9-97  3«>3 

5 
5 
4 
5 

5 
4 
3 

2 

I 

20 

3° 
4° 
So 

1.7 

2-5 
3-3 
4.2 

i-3 

2.O 
2.7 

3-3 

60 

9-53  405 

35 

9.56  107 

4° 

0-43  893 

9-97  299 

o 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.Tang. 

L.  Sin. 

d. 

r 

Pi 

op.  1 

Pts. 

70< 


20< 


/• 

L.  Sin. 

(1. 

L.Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

Pi 

op. 

Pts. 

o 

2 

3 
4 

9-53  4°5 
9-53  44° 
9-53  475 
9-53  509 
9-53  544 

35 
35 
34 
35 

9.56  107 
9.56  146 
9.56  185 
9.56  224 
9.56  264 

39 
39 
39 
40 

0-43  893 
0-43  854 
0.43  815 
0.43  776 
0.43  736 

9.97  299 
9.97  294 
9-97  289 
9.97  285 
9.97  280 

5 

5 
4 

5 

GO 

59 
58 
57 
56 

6 

7 

40 

4.0 
4-7 

39 

3-9 
4.6 

5 
6 

7 

8 

9 

9-53  578 
9-53  613 
9-53  647 
9-53  682 
9-53  7i6 

35 
34 
35 
34 

9-56  303 
9-56  342 
9.56  381 
9.56  420 
9-56  459 

39 
39 
39 
39 

0.43  697 
0.43  658 
0.43  619 
0.43  580 
°-43  54i 

9-97  276 
9-97  271 
9.97  266 
9.97  262 
9-97  257 

5 
5 
4 
5 

55 
54 
53 
52 

5i 

8 
9 

10 

20 
3° 

5-3 
6.0 

6-7 
13-3 

2O.O 

5-2 

5,9 
6-5 
13.0 

19-5 

1O 

ii 

12 
13 
14 

9-53  75i 
9-53  785 
9-53  819 
9-53  854 
9.53  888 

34 
34 
35 
34. 

9.56  498 
9-56  537 
9-56  576 
9.56  615 
9-56  654 

39 
39 
39 
39 

0.43  502 

0-43  463 
0.43  424 

0-43  385 
o-43  346 

9-97  252 
9.97  248 
9-97  243 
9.97  238 
9.97  234 

4 
5 
5 
4 

50 

49 
48 

47 
46 

40 
50 

2b.7 
33-3 

38 

26.0 

32.5 

37 

15 

16 

17 
18 

19 

9-53  922 
9-53  957 
9-53  99i 
9-54  025 
9-54  059 

35 
34 
34 
34 

9-56  693 
9-56  732 
9.56  771 
9.56  810 
9.56  849 

39 
39 
39 
39 
•38 

0-43  307 
0.43  268 
0.43  229 
0.43  190 
o-43  I51 

9.97  229 
9-97  224 
9.97  220 
9-97  215 

9.97  210 

5 
4 
5 
5 

45 
44 
43 
42 

4i 

6 

7 
8 

9 

10 

3-8 
4-4 
5-1 
5-7 
6-3 

3-7 
4-3 
4-9 
5-6 

6.2 

20 

21 
22 
23 

24 

9-54  093 
9-54  127 
9-54  161 
9-54  195 
9-54  229 

34 
34 
34 
34 

9.56  887 
9.56  926 
9-56  965 
9-57  004 
9.57  042 

39 
39 
39 
38 

0-43  "3 
0.43  074 

0-43  035 
0.42  996 
0.42  958 

9.97  206 
9-97  201 

9-97  196 
9.97  192 
9.97  187 

5 
5 
4 
5 

40 

39 
38 
37 
36 

20 

3° 
40 

50 

12.7 
19.0 
25-3 
31-7 

12.3 

18-5 
24-7 
30.8 

25 
26 
27 
28 
29 

9-54  263 
9-54  297 
9-54  33i 
9-54  365 
9-54  399 

34 
34 
34 
34 

9-57  081 
9-57  120 
9-57  158 
9-57  197 
9-57  235 

39 
39 
38 
39 
38 

0.42  919 
0.42  880 
0.42  842 
0.42  803 
0.42  765 

9.97  182 
9.97  178 

9-97  173 
9.97  168 
9.97  163 

4 

5 
5 
5 

35 
34 
33 
S2 
3i 

- 

3. 

6      3 
7      4 
8      4 

5 

•5 
.1 

•7 

30 

3i 
32 
33 
34 

9-54  433 
9-54  466 
9-54  5°o 
9-54  534 
9-54  567 

33 
34 
34 
33 

9-57  274 
9-57  312 
9-57  35i 
9-57  389 

9.57  428 

39 
38 
39 
38 

39 
08 

0.42  726 
0.42  688 
0.42  649 
0.42  611 
0.42  572 

9-97  159 
9-97  154 
9-97  149 
9-97  145 
9.97  140 

5 
5 
4 
5 

30 

29 
28 
27 
26 

3 

< 

9      5 
o     5 

0      II 

o    17 

^  23 

•3 

.8 
•7 
•5 
-3 

35 
36 
37 
38 
39 

9.54  601 
9-54  635 
9-54  668 
9.54  702 
9-54  735 

34 
34 
33 
34 
33 

9-57  466 
9-57  504 
9-57  543 
9-57  58i 
9-57  619 

3° 
38 
39 
38 
38 

0-42  534 
0.42  496 
0.42  457 
0.42  419 
0.42  381 

9-97  135 
9.97  130 
9.97  126 
9.97  121 
9.97  116 

5 
4 
5 
5 

25 
24 
23 

22 
21 

6 

34 

3-4 

33 

3-3 

4O 

41 

42 
43 
44 

9-54  769 
9-54  802 
9-54  836 
9-54  869 
9-54  903 

34 
33 
34 
33 
34 

9-57  658 
9-57  696 
9-57  734 
9-57  772 
9.57810 

39 
38 
38 
38 
38 

0.42  342 
0.42  304 
0.42  266 
0.42  228 
0.42  190 

9-97  "I 
9-97  i°7 
9.97  102 
9-97  097 
9-97  092 

4 
5 
5 
5 

2O 

19 

18 

17 
16 

7 
8 

9 

10 
20 

3O 

4.0 
4-5 
5-i 
5-7 
H-3 
17  o 

3-9 
4-4 
5-o 

5-5 

II.O 

16  < 

45 
46 

47 
48 

49 

9-54  936 
9-54  969 
9-55  003 
9-55  036 
9-55  069 

33 
34 
33 
33 

9-57  849 
9-57  887 
9-57  925 
9-57  963 
9.58  ooi 

38 
38 
38 
38 

,0 

0.42  151 
0.42  113 
0.42  075 
0.42  037 
0.41  999 

9-97  087 
9-97  083 
9-97  078 
9-97  073 
9.97  068 

4 
5 
5 
5 

15 
14 

*3 

12 
II 

40 
5° 

22.7 
28.3 

22.0 

27-5 

5O 

5i 

52 
53 
54 

9-55  102 
9-55  IS6 
9-55  169 
9.55  202 

9-55  235 

33 
34 
33 
33 
33 

9-58  039 
9.58  077 
9-58  115 
9-58  153 
9.58  191 

3° 
38 
38 
38 
38 

_Q 

0.41  961 
0.41  923 
0.41  885 
0.41  847 
0.41  809 

9.97  063 
9-97  059 
9-97  054 
9-97  049 
9.97  044 

4 
5 
5 
5 

10 

9 
8 

7 
6 

6 

7 
8 

9 
10 

0.5 
0.6 
0.7 
0.8 
0.8 

0.4 

0.5 
0.5 
0.6 
0.7 

55 
56 
57 
58 
59 

9-55  268 
9-55  301 
9-55  334 
9-55  367 
9-55  400 

33 
33 
33 
33 
33 

9.58  229 
9.58  267 
9-58  304 
9.58  342 
9.58  380 

38 
38 
37 
38 
38 

_Q 

0.41  771 

0.41  733 
0.41  696 
0.41  658 
0.41  620 

9-97  039 
9-97  035 
9-97  030 
9-97  025 
9.97  020 

4 
5 
5 
5 

5 
4 
3* 

2 

I 

20 
30 
4<> 

50 

1-7 

2-5 

3-3 

4-2 

i-3 

2.0 
2.7 

3-3 

GO 

9-55  433 

33 

9-58  418- 

38 

0.41  582 

9-97  015 

O 

L.  Cos. 

d. 

L.  Coif. 

c.  d. 

L.Tang. 

I,.  Sin. 

d. 

r 

Pr 

«>p,    1 

Ms. 

69( 


r 

L.  Sin. 

d. 

L.Tang. 

c.  d.  L.  Cotg. 

L.  Cos. 

d. 

Prop.  Pts. 

O 

i 

2 

3 

4 

9-55  433 
9-55  466 
9-55  499 
9-55  532 
9-55  564 

33 
33 
33 
32 
33 
33 
33 
32 
33 
33 
32 
33 
32 
33 
32 

33 
32 
33 
32 
32 
33 
32 
32 
33 
32 
32 
32 
32 
32 
33 
32 
32 
32 
32 

9.58  418 
9-58  455 
9-58  493 
9.58  53i 
9.58  569 

37 
38 
38 
38 
37 
38 
37 
38 
38 
37 
38 
37 
38 
37 
37 
38 
37 
38 
37 
37 
37 
38 
37 
37 
37 
37 
38 
37 
37 
37 
37 
37 
37 
37 
37 
37 
37 
36 
37 
37 
37 
37 
36 
37 
37 
37 
36 
37 
37 
36 

37 
36 
37 
36 
37 
36 
37 
36 
37 
36 

0.41  582 

0.41  545 
0.41  507 
0.41  469 
0.41  431 

9-97  015 
9.97  010 
9.97  005 
9.97  ooi 

9.96  996 

5 
5 
4 
5 
5 
5 
5 
5 
5 
5 
4 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 
4 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 
5 

60 

59 
58 
57 
56 

6 
7 

38 
3-8 
4-4 
S-i 
5-7 
6.3 
12.7 
19.0 
25-3 
31-7 

36 
3-6 

4-2 

4.8 

5-4 
6.0 

12.0 

18.0 
24.0 
30.0 

'9 

6   3 
7   3 
8   4 

9   4 
o  5 

0   10 

o  16 

O   21 

o  26 

31 

iS 

4.1 

4.7 

5-2 

10.3 

15.5 
20.7 

25.8 

5 

0-5 
0.6 
0.7 
0.8 
0.8 

1-7 
2.5 

3-3 
4.2 

37 

3-7 
4-3 
4-9 
5-6 

6.2 

12.3 
18.5 
24.7 
30.8 

33 

3-3 
3-9 
4.4 
5-0 
5.5 

II.O 

16.5 

22.O 

27-5 

2 
.2 

•7 
•3 

.8 

•3 
•7 

.0 

•3 
•7 

6 
0.6 
0.7 
0.8 
0.9 

I.O 
2.0 
3-0 
4.0 

5-0 

4 

0.4 
o.S 

0-5 
0.6 
0.7 
1-3 

2.0 
2.7 

3-3 

5 
6 

7 

8 

9 

9-55  597 
9-55  630 
9-55  663 
9-55  695 
9-55  728 

9.58  606 
9.58  644 
9.58  681 
9.58  719 
9-58  757 

0.41  394 
0.41  356 
0.41  319 
0.41  281 
0.41  243 

9.96  991 

9.96  986 
9.96  981 

9.96  976 
9.96  971 

55 
54 
53 
52 
Si 

8 
9 

10 
20 
30 

10 

ii 

12 
13 
14 

9-55  761 
9-55  793 
9-55  826 
9-55  858 
9-55  891 

9-58  794 
9.58  832 
9.58  869 
9.58  907 
9.58  944 

0.41  206 
0.41  168 
0.41  131 
0.41  093 
0.41  056 

9.96  966 
9.96  962 
9-96  957 
9.96  952 
9.96  947 

50 

49 
48 
47 
46 

40 
50 

6 

8 
9 

10 
20 

30 
40 

50 

I 

c 

! 

c 

6 

8 
9 

10 

20 

30 
40' 

50 

6 

7 

8 

9 

10 
20 
30 
40 
50 

15 

16 
17 
18 

19 

9-55  923 
9-55  956 
9-55  988 

9.56  021 
9-56  053 

9.58  981 
9-59  OI9 
9-59  056 
9-59  °94 
9-59  131 

0.41  019 
0.40  981 
0.40  944 
0.40  906 
0.40  869 

9.96  942 
9-96  937 
9.96  932 
9.96  927 
9.96  922 

45 
44 
43 
42 

41 

2O 

21 
22 

23 
24 

9.56  085 

9.56  118 
9.56  150 
9.56  182 
9.56  215 

9.59  168 
9-59  205 
9-59  243 
9.59  280 

9-59  317 

0.40  832 
0.40  795 
0.40  757 
0.40  720 
0.40  683 

9.96  917 
9.96  912 
9-96  907 
9.96  903 
9.96  898 

40 

39 
38 

1 

25 
26 

27 
28 
29 

9.56  247 
9.56  279 
9-56311 
9-56343 
9-56  375 

9-59  354 
9-59  39i 
9-59  429 
9-59  466 
9-59  503 

0.40  646 
0.40  609 
0.40  571 

o-40  534 
0.40  497 

9.96  893 
9.96  888 
9-96  883 
9.96  878 
9.96  873 

35 
34 
33 
32 
3i 

30 

3i 
32 
33 
34 

9.56  408 
9.56  440 
9.56  472 
9.56  504 
9-56  536 

9-59  540 
9-59  577 
9-59  614 
9-59  651 
9-59  688 

0.40  460 
0.40  423 
0.40  386 
0.40  349 
0.40  3-12 

9.96  868 
9.96  863 
9.96  858 
9-96  853 
9.96  848 

30 

29 
28 
27 
26 

35 
36 
37 
38 
39 

9-56  568 
9.56  599 
9.56  631 
9.56  663 
9o6  695 

32 

3i 
32 
32 
32 
32 
32 
3i 
32 
32 
32 
3i 
32 
31 
32 
32 
3i 
32 
3i 
3i 
32 

3i 
32 
3i 
3i 

9-59  725 
9-59  762 
9-59  799 
9-59  835 
9-59  872 

0.40  275 
0.40  238 
0.40  201 
0.40  165 
0.40  128 

9.96  843 
9.96  838 
9.96  833 
9.96  828 
9.96  823 

25 
24 
23 

22 
21 

40 

4i 
42 

43 

44 

9.56  727 
9-56  759 
9.56  790 
9.56  822 
9-56  854 

9.59  909 
9-59  946 
9-59  983 
9.60  019 
9.60  056 

0.40  091 
0.40  054 
0.40  017 
0.39  981 
0.39  944 

9.96  818 
9.96  813 
9.96  808 
9.96  803 
9.96  798 

5 
5 
5 
5 

20 

19 
18 

17 
16 

45 
46 
47 
48 
49 

9.56  886 
9.56  917 
9-56  949 
9.56  980 
9-57  012 

9.60  093 
9.60  130 
9.60  166 
9.60  203 
9.60  240 

0.39  907 
0.39  870 

0-39  834 
0.39  797 
0.39  760 

9-96  793 
9.96  788 
9.96  783 
9.96  778 
9.96  772 

5 
5 
5 
6 

15 
14 
13 

12 
II 

50 

5i 
52 
53 
54 

9.57  044 

9-57  075 
9.57  107 
9-57  138 
9-57  169 

9.60  276 
9.60  313 
9.60  349 
9.60  386 
9.60  422 

0.39  724 
0.39  687 
0.39  651 
0.39  614 
0-39  578 

9-96  767 
9.96  762 
9-96  757 
9.96  752 
9.96  747 

5 
5 
5 
5 
5 
5 
5 
5 
5 
5 

10 

9 
8 

7 
6 

55 
56 
57 
58 
59 

9-57  201 
9-57  232 
9-57  264 
9-57  295 
9-57  326 

9.60  459 
9.60  495 
9.60  532 
9.60  568 
9.60  605 

0-39  54i 
o-39  5°5 
0.39  468 

o-39  432 
o-39  395 

9.96  742 
9.96  737 
9.96  732 
9-96  727 
9.96  722 

5 
4 
3 

2 

I 

60 

9-5.7  358 

32 

9.60  641 

°-39  359 

9-96  717 

5 

O 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.Tang. 

L.  Sin. 

d. 

r 

Prop.  Pts. 

68< 


44 


22< 


r 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

L.  Cotg. 

L,.  Cos. 

d. 

I*  i 

op.  1 

Pts. 

O 

i 

2 

3 
4 

9-57  358 
9-57  389 
9-57  420 
9-57  45i 
9-57  482 

31 
31 

31 
3» 

9.60  641 
9.60  677 
9.60  714 
9.60  750 
9.60  786 

36 

37 
36 
36 

o-39  359 
0,39  323 
0.39  286 
0.39  250 
0.39  214 

9.96  717 
9.96  711 
9.96  706 
9.96  701 
9.96  696 

6 
5 
5 
5 

GO 

59 
58 
57 
56 

6 
7 

37 
3-7 
4-3 

36 

3-6 
4.2 

5 
6 

7 

8 

9 

9-57  5H 
9-57  545 
9-57  576 
9-57  607 
9-57  638 

3» 
3» 
3i 
3i 

9.60  823 
9.60  859 
9.60  895 
9.60  931 
9.60  967 

37 
36 
36 
36 
36 

0.39  177 
0.39  141 
0.39  105 
0.39  069 
o-39  033 

9.96  691 
9.96  686 
9.96  681 
9.96  676 
9.96  670 

5 
5 
5 
6 

55 
54 
53 
52 
5i 

8 
9 

10 
20 
30 

4.9 
5-6 

6.2 

12.3 
18.5 

4.8 
& 

I2.O 

18.0 

10 

ii 

12 
13 
14 

9.57  669 
9-57  700 
9-57  73i 
9-57  762 
9-57  793 

31 
3i 
3' 
3i 
3i 

9.61  004 
9.61  040 
9.61  076 

9.61   112 
9.61   148 

37 
36 
36 
36 
36 

ofi 

0.38  996 
0.38  960 
0.38  924 
0.38  888 
0.38  852 

9.96  665 
9.96  660 
9-96  655 
9.96  650 
9.96  645 

5 
5 
5 
5 

5O 

49 
48 
47 
46 

40 
50 

24.7 
30.8 

3 

24.0 

30.0 
5 

15 

16 

17 
18 

19 

9-57  824 
9-57  855 
9-57  885 
9-57  916 
9-57  947 

3i 
30 
3i 
3i 

9.61   184 
9.61  22O 
9.61  256 
9.61  292 
9.6l  328 

3° 
36 
36 
36 
36 

0.38  816 
0.38  780 
0.38  744 
0.38  708 
0.38  672 

9.96  640 
9.96  634 
9.96  629 
9.96  624 
9.96  619 

6 
5 
5 
5 

45 
44 
43 
42 
41 

3 

6      3 
7      4 
8      4 
9      5 
to      5 

•5 
.1 

•7 
-3 
.8 

20 

21 
22 

23 
24 

9-57  978 
9.58  008 
9-58  039 
9.58  070 
9.58  101 

31 
30 
31 
31 
3i 

9.61  364 
9.61  400 
9.6l  436 
9.6l  472 
9.6l  508 

3° 
36 
36 
36 
36 
if> 

0.38  636 
0.38  600 
0.38  564 
0.38  528 
0.38  492 

9.96  614 
9.96  608 
9.96  603 
9.96  598 
9  96  593 

6 
5 
5 
5 

4O 

39 
38 
37 
36 

i 

JO      II 

jo    17 
\o    23 
;o    29 

•7 
•5 
•3 

.2 

25 
26 

27 
28 
29 

9-58  131 
9.58  162 
9.58  192 
9.58  223 
9-58  253 

3i 
30 
3i 
3" 

9.61  544 
9.61  579 
9.61  615 
9.61  651 
9.61  687 

35 
36 
36 
36 

0.38  456 
0.38  421 
0.38  385 
0.38  349 
0.38  313 

9  96  588 
9.96  582 

9-96  577 
9.96  572 
9.96  567 

6 
5 
5 

5 

35 
34 
33 
32 
3i 

6 

7 
8 

3* 

3-2 

3-7 
4-3 

31 

H 

4.I 

30 

3i 

32 
33 
34 

9.58  284 
9-58  3H 
9-58  345 
9-58  375 
9.58  406 

31 
30 
3i 
30 
3i 

9.61  722 
9.61  758 
9.61  794 
9.61  830 
9.61  865 

35 
36 
36 
36 
35 

0.38  278 
0.38  242 
0.38  206 
0.38  170 
0-38  135 

9.96  562 
9-96  556 
9-96  55i 
9.96  546 
9.96  541 

6 
5 
5 
5 

3O 

29 
28 
27 
26 

9 

10 
20 

30 
40 

CQ 

4.8 

5-3 
10.7 
16.0 
21.3 

26  7 

4-7 

5-2 

10.3 

15-5 
20.7 
2c  8 

35 
36 
37 
38 
39 

9-58  436 
9.58  467 
9-58  497 
9-58  527 
9-58  557 

3° 
3» 
3° 
3<> 
30 

9.61  901 
9.61  936 
9.61  972 
9.62  008 
9.62  043 

30 
35 
36 
36 
35 
ofi 

0.38  099 
0.38  064 
0.38  028 
0.37  992 
o.37  957 

9-96  535 
9-96  530 
9-96  525 
9.96  520 
9.96  514 

5 
5 
5 
6 

25 
24 

23 

22 
21 

6 

30 

3-0 

29 
2.9 

4O 

4i 
42 
43 
44 

9-58  588 
9.58  618 
9.58  648 
9.58  678 

9.58  709 

31 
30 
30 
3<> 
3« 

9.62  079 
9.62  114 
9.62  150 
9.62  185 

9.62  221 

3° 
35 
36 
35 
36 

0.37  921 
0.37  886 
0.37  850 
0-37  815 
0.37  779 

9.96  509 
9.96  504 
9.96  498 

9-96  493 
9.96  488 

5 
6 
5 
5 

2O 

19 

18 

17 
16 

7 
8 

9 

10 

20 
30 

3-5 
4.0 

4-5 
5-0 

IO.O 

15.0 

3-4 
3-9 
4-4 
4.8 

9-7 

14  c 

45 
46 

47 
48 
49 

9-58  739 
9.58  769 
9-58  799 
9.58  829 
9-58  859 

3° 
3° 
30 
3<> 
30 

9.62  256 
9.62  292 
9.62  327 
9.62  362 
9.62  398 

35 
36 
35 
35* 
36 

0-37  744 
0.37  708 
0.37  673 
0.37  638 
0.37  602 

9.96  483 
9-96  477 
9.96  472 
•  9.96  467 
9.96  461 

6 
5 
5 
6 

15 
14 
13 

12 
II 

40 
So 

20.0 
25.0 

5 

J9-3 
24.2 

50 

5i 
52 
53 
54 

9.58  889 
9-58  919 
9-58  949 
9-58  979 
9.59009 

30 

3° 
3° 
30 
3° 

9.62  433 
9.62  468 
9.62  504 
9-62  539 
9.62  574 

35 
35 
36 
35 
35 

0-37  567 
o.37  532 
0.37  496 
0.37  461 
0.37  426 

9.96  456 
9.96  451 
9-96  445 
9.96  440 

9-96  435 

5 
6 
5 
5 

10 

9 
8 

7 
6 

6 

7 
8 

9 
10 

0.6 
0.7 
0.8 
0.9 

I  O 

o.S 
0.6 
0.7 
0.8 
08 

55 
56 
57 
58 
59 

9-59  <>39 
9.59069 
9-59  098 
9-59  "8 
9-59  158 

3° 
3<> 
»9 
30 
3<> 

9.62  609 
9.62  645 
9.62  680 
9-62  715 
9.62  750 

35 
36 
35 
35 
35 

o  37  391 
0-37  355 
0.37  320 
0.37  285 
0.37  250 

9.96  429 
9.96  424 
9.96  419 
9  96  413 
9.96  408 

5 
5 
6 
5 

5 
4 
3 

2 

I 

20 

3° 

40 
50 

2.0 

3-o 

4.0 

5-0 

i-7 
2-5 
3-3 
4.2 

60 

9-59  1  88 

3° 

9.62  785 

35 

0.37  215 

9.96  403 

5 

O 

L.  Cos. 

d. 

1,.  Cotff. 

c.  d. 

L.  Ta  UK. 

L.  Sin. 

d. 

r 

Pr 

op.  I 

'ts. 

67 


23' 


45 


/• 

L.  Sin. 

d. 

L.Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

Prop.  Pts. 

0 

I 

2 

3 

4 

9-59  188 
9-59  218 
9-59  247 
9-59  277 
9-59  3°7 

3° 
29 
30 
3° 

29 

3<> 
30 
29 
30 
29 

3° 
29 

3° 
29 

9.62  785 
9.62  820 
9.62  855 
9.62  890 
9.62  926 

35 
35 
35 
36 
35 
35 
35 
35 
35 
34 
35 
35 
35 
35 
35 
35 
34 
35 
35 
35 
35 
34 
35 
35 
34 
35 
34 
35 
35 
34 
35 
34 
35 
34 
35 
34 
35 
34 
34 
35 
34 
34 
35 
34 
34 
35 
34 
34 
34 
34 
35 
34 
34 
34 
34 
34 
34 
34 
34 
34 

0.37  215 
0.37  180 

0-37  M5 
0.37  no 

0.37  074 

9.96  403 
9-96  397 
9.96  392 
9.96  387 
9.96  381 

6 
5 
5 
6 

5 
6 
5 
5 
6 
5 
6 
5 
5 
6 
5 
6 
5 
6 
5 
6 

5 
5 
6 
5 
6 

5 
6 
5 
6 

6O 

59 

58 
57 
56 

6 
7 

< 
< 

i 
ii 
U 

Q.L 

3< 

6 

7 
8 

9 

10 
20 
30 
1° 
50 

3 

• 

\ 

A 
4 
5 

1C 

15 

2C 
25 

6 

7 
8 

9 

[0 
>0 

5° 
p 
50 

< 

c 

0 
0 

o 

2 

3 
4 

5 

16 
j.6 

1-2 

j.8 

5-4 

).0 
J.O 

5.o 

[.0 
).0 

3 

-1 
4 

c 
c 

IJ 
«3 

22 
2g 

0 

.0 

•5 

.0 

•5 

.0 
.0 

.0 

.0 

.0 

2 

2 

3 
3 
4 
4 
9 
14 
18 
23 

i 

.6 

•7 

.8 

•9 

.0 

.0 

.0 
.0 

.0 

35 
3-5 
4.1 

4-7 
5-3 
5-8 
11.7 
17-5 
23-3 
29.2 

4 
•4 

^.0 

kS 
I 
.7 

•3 
.0 

•7 
•3 

29 

2.9 
3-4 
3-9 
4-4 
4.8 

9-7 
14-5 
19-3 
24.2 

8 
.8 
•3 

•7 

.2 

•7 

•3 
.0 

•7 
•3 

5 

0-5 
06 
0.7 
0.8 
0.8 
1-7 
2-5 
3-3 

4-2 

5 
6 

7 
8 
9 

9-59  336 
9-59  366 
9-59  396 
9-59  425 
9-59  455 

9.62  961 
9.62  996 
9.63  031 
9.63  066 
9.63  101 

0.37  039 
0.37  004 
0.36  969 

0-36  934 
0.36  899 

9.96  376 
9.96  370 
9-96  365 
9.96  360 
9-96  354 

55 
54 
53 
52 
5i 

8 

9 
10 

20 
30 

1O 

ii 

12 
13 

14 

9.59  484 
9-59  5i4 
9-59  543 
9-59  573 
9-59  602 

9-63  135 
9.63  170 
9.63  205 
9.63  240 
9-63  275 

0.36  865 
0.36  830 

0-36  795 
0.36  760 
0.36  725 

9-96  349 
9-96  343 
9-96  338 
9-96  333 
9.96  327 

50 

49 
48 

47 
46 

40 
50 

6 

7 
8 

9 

10 
20 

3° 

40 
50 

J 

i 

1 

6 

8 
9 

10 

20 

30 
40 

50 

15 

16 

17 
18 

19 

9-59  632 
9-59  661 
9-59  690 
9-59  720 
9-59  749 

29 
29 

3<> 

29 
29 
30 
29 
29 
29 
29 
30 
29 
29 
29 

9.63  310 
9-63  345 
9-63  379 
9.63  414 
9.63  449 

0.36  690 
0.36  655 
0.36  621 
0.36  586 
o-S6  55i 

9.96  322 
9.96  316 
996311 

9-96  3<>5 
9.96  300 

45 
44 
43 
42 
4i 

2O 

21 
22 

23 
24 

9-59  778 
9-59  808 
9-59  837 
9-59  866 
9-59  895 

9.63  484 
9-63  519 
9-63  553 
9-63  588 
9.63  623 

0.36  516 
0.36  481 
0.36  447 
0.36  412 
0.36  377 

9.96  294 
9.96  289 
9.96  284 
9.96  278 
9.96  273 

40 

39 

38 
37 
36 

2S 

26 

27 

28 

29 

9-59  924 
9-59  954 
9-59  983 

9.60  012 
9.60  041 

9-63  657 
9.63  692 
9.63  726 
9.63  761 
9.63  796 

0-36  343 
0.36  308 
0.36  274 
o  36  239 
0.36  204 

9.96  267 
9.96  262 
9.96  256 
9.96  251 
9.96  245 

35 
34 
33 
32 
3i 

30 

3i 
32 
33 
34 

9.60  070 
9.60  099 
9.60  128 
9.60  157 

9.60  186 

29 
29 
29 
29 

9.63  830 
9.63  865 
9.63  899 

9-63  934 
9.63  968 

0.36  170 
0.36  135 
0.36  101 
0.36  066 
0.36  032 

9.96  240 
9.96  234 
9  96  229 
9.96  223 
9.96  218 

6 
5 
6 

5 
g 

30 

29 
28 

27 
26 

3 

37 
38 
39 

9.60  215 
9.60  244 
9.60  273 
9.60  302 
9.60  331 

29 
29 
29 
29 
29 
28 
29 
29 
29 
28 
29 
29 
29 
28 
29 
28 
29 
29 
28 
29 
28 

9.64  003 
9.64  037 
9.64  072 
9.64  106 
9.64  140 

o-35  997 
0-35  963 
0.35  928 

o-35  894 
0.35  860 

9.96  212 
9.96  207 
9.96  2OI 
9.96  196 
9.96  190 

5 
6 

5 
6 
5 
6 
5 
6 
6 

25 
24 

23 

22 
21 

40 

4i 
42 

43 

44 

9-6o  359 
9.60  388 
9.60  417 
9.60  446 
9.60  474 

9.64  175 
9.64  209 
9.64  243 
9.64  278 
9.64  312 

0.35  825 
o-35  79i 
o-35  757 
0.35  722 
0.35  688 

9.96  185 
9.96  179 
9.96  I74 

9.96  168 
9.96  162 

20 

J9 
18 

17 
16 

45 
46 

47 
48 
49 

9.60  503 
9.60  532 
9.60  561 
9.60  589 
9.60  618 

9.64  346 
9.64  381 
9.64  415 

9  64  449 
9.64  483 

0-35  654 
0.35  619 

°-35  585 
o-35  55i 
035  5i7 

9.96  157 

9  96  151 
9.96  146 
9.96  140 
9-96  135 

6 
5 
6 
5 

15 
14 
13 

12 
II 

50 

5i 
52 
53 
54 

9.60  646 
9.60  675 
9.60  704 
9.60  732 
9.60  761 

9.64  517 

9-64  552 
9.64  586 
9.64  620 
9.64  654 

0-35  483 
0-35  448 
0-35  414 
0.35  380 
0.35  346 

9.96  129 
9.96  123 
9.96  118 
9.96  112 
9.96  107 

6 
5 
6 
5 
6 
6 
5 
6 

5 

10 

9 
8 

7 
6 

55 
56 
57 
58  . 
59 

9.60  789 
9.60  818 
9.60  846 
9.60  875 
9.60  903 

29 
28 
29 
28 

9.64  688 
9.64  722 
9  64  756 
9.64  790 
9.64  824 

0.35  312 
0.35  278 

0-35  244 
0.35  210 
0.35  176 

9.96  101 

9.96  095 
9.96  090 

9.96  084 

9.96  079 

5 
4 
3 

2 

I 

6O 

9.60  931 

9.64  858 

o-35  142 

9.96  073 

0 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.  Tang. 

L.  Sin. 

d. 

/• 

Prop.  Pts. 

66< 


46 


24' 


/ 

L.  Sin. 

d. 

L.Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

Proj 

..   1 

Pts. 

0 

I 

2 

3 
4 

9.60  931 
9.60  960 
9.60  988 
9.61  016 
9.61  045 

29 
28 
28 
29 

28 

9.64  858 
9.64  892 
9.64  926 
9.64  960 
9.64  994 

34 
34 
34 
34 

0-35  142 
0.35  108 
0-35  074 
0.35  040 
0.35  006 

9.96  073 
9.96  067 
9.96  062 
9.96  056 
9.96  050 

6 
5 
6 
6 

6O 

59 
58 

57 
56 

3 

6      2 
7      4 

4 

•4 

.0 

33 
3-3 
3-9 

6 

7 
8 
9 

9.61  073 
9.61  101 
9.61  129 
9.61  158 
9.61  186 

28 
28 
29 
28 
?s 

9.65  028 
9.65  062 
9-65  096 
9.65  130 
9.65  164 

34 
34 
34 
34 
34 

0.34  972 
o-34  938 
0.34  904 
0.34  870 
0.34  836 

9.96  045 
9.96  039 
9.96  034 
9.96  028 

q.q6  022 

6 
5 
6 
6 

55 
54 
53 
52 
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34 
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0.30  226 
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9-95  173 
9.95  167 
9.95  160 
9-95  154 

3O 

29 
28 
27 
26 

35 
36 
37 
38 
39 

9.65  079 
9.65  104 
9.65  I3o 

9-65  155 
9.65  1  80 

25 
26 
25 
25 

9.69  932 
9.69  963 

9-69  995 
9.70  026 
9.70  058 

0.30  068 
0.30  037 
0.30  005 
0.29  974 
0.29  942 

9-95  148 
9-95  141 
9-95  135 
9-95  129 
9-95  122 

25 
24 
23 

22 
21 

40 

42 
43 
44 

9.65  205 
9.65  230 
9.65  255 
9.65  281 
9.65  306 

25 
25 
25 
26 
25 
25 
25 
25 
25 
25 

9.70  089 

9.70  121 
9.70  152 
9.70  184 
9.70  215 

0.29  911 
0.29  879 
0.29  848 
0.29  816 
0.29  785 

9.95  116 
9-95  1  10 
9-95  103 
9-95  097 
9-95  090 

20 

19 
18 

17 

16 

45 
46 
47 
48 
49 

9.65  331 
9-65  356 
9-65  381 
9.65  406 

9.70  247 
9-70  278 
9.70  309 
9-70  341 
9.70  372 

0.29  753 
0.29  722 
0.29  691 
0.29  659 
0.29  628 

9.95  084 
9-95  078 
9-95  071 
9-95  065 
9-95  059 

6 
7 
6 
6 

15 
14 
13 

12 
II 

50 

5i 

52 
53 
54 

9.65  456 
9.65  481 
9.65  506 
9-65  53i 
9-65  556 

25 
25 
25 
25 
25 
24 
25 
25 
25 
25 

9.70  404 

9-70  435 
9.70  466 
9.70  498 
9.70  529 

0.29  596 
0.29  565 
0-29  534 
0.29  502 
0.29  471 

9-95  052 
9-95  046 
9-95  039 
9-95  033 
9-95  027 

6 
7 
6 
6 

10 

9 

8 
7 
6 

55 
56 
57 
58 
59 

9-65  58o 
9.65  605 
9.65  630 
9-65  655 
9.65  680 

9.70  560 
9.70  592 
9.70  623 
9.70  654 
9.70  685 

0.29  440 
0.29  408 
0.29  377 
0.29  346 
0.29  315 

9-95  020 
9-95  014 
9.95007 
9-95  ooi 
9-94  995 

6 
7 
6 
6 

5 
4 
3 

2 
I 

00 

9.70  717 

0.29  283 

9-94  988 

0 

L.  Cos. 

d. 

L.Cotp. 

c.  d. 

L.Tnng. 

L.  Sin. 

d. 

f 

Prop.  Pts. 

63C 


27< 


49 


/• 

L.  Sin. 

d. 

L.Tang.  c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

Prop.  Pts. 

o 

I 

2 

3 

4 

9-65  7°5 
9.65  729 

9-65  754 
9-65  779 
9.65  804 

24 
25 
25 
25 
24 

25 
25 
24 
25 
25 
24 
25 
24 
25 

9.70  717 
9.70  748 
9.70  779 
9.70  810 
9.70  841 

31 
31 
3i 
3i 
32 

3i 
3i 
3i 
31 
3i 
3i 
3i 
31 
32 
3i 
31 
3i 
3i 
3i 
3i 
3i 
3i 
30 
31 
3i 
3i 
3i 
3i 
3i 
3i 
3i 
30 
3i 
3i 
3i 
31 
3° 
3i 
3i 
30 

3i 
3i 
3i 
30 
3i 
3i 
3° 
3i 
30 
3i 
3i 
30 
3i 
30 
3i 
3° 
3i 
3° 
3i 
3° 

0.29  283 
0.29  252 

O.29  221 
0.29  190 
0.29  159 

9.94  988 
9.94  982 
9-94  975 
9-94  969 
9.94  962 

6 

7 
6 

7 

6 

7 

6 

7 
6 
7 
6 
6 

7 

6 

7 
6 
7 
7 
6 

7 
6 
7 
6 
7 
6 

7 
6 
7 
7 
6 

7 
6 

7 

6 

7 

7 

6 

7 

6 

7 
7 
6 
7 
7 
6 

7 
7 
6 
7 
7 
6 
7 
7 
6 

7 

7 
6 

7 
7 

GO 

59 
58 
57 
56 

6 

7 
8 

9 

10 

20 

30 
40 

So 

3 
Z 

t 
i 

6 

7 
8 

9 

10 
20 

30 

40 

50 

I 

2 

3 
A 
5 

6 

7 
8 

9 

10 
20 

3° 

40 
50 

3 

' 
t 
i 

1C 

ie 

2] 

Zf 

6 

7 
8 
9 

0 
20 
!0 
P 

o 

3 
2 
2 

2 
t 
A 

8 

12 

16 

2C 

6 

7 
8 

9 

0 

o 
o 

0 
0 

0 
0 

o 

I 
I 

2 

3 

4 

5 

2 

•2 

•  7 
[-3 
\& 
•3 
'•7 

).O 

•3 

•7 

a 

4 
t 
t 

1C 

If 

2C 

2^ 

5 

•5 
•9 
•3 
.8 

.2 

-3 

•5 
•7 
.8 

a 

2 
2 

3 
3 
3 
7 
ii 

IS 
19 

7 

•7 
.8 

•9 
.1 

.2 

•3 

•5 

•7 
.8 

31 
3-1 
3.6 
4.1 
4-7 

5-2 

10.3 

15-5 
20.7 
25.8 

0 
.0 

•5 

^.0 

(-5 

.0 
).0 
.0 
).0 
.0 

24 

2.4 

2.8 
3-2 

3.6 
4.0 
8.0 

12.0 

16.0 

20.0 

3 
•3 
•7 
.1 

-5 
.8 
•7 
•5 
•3 

.2 

6 
0.6 
0.7 
0.8 
0.9 

I.O 
2.0 

3-o 

4.0 
5.0 

5 
6 

7 
8 

9 

9.65  828 
9-65  853 
9.65  878 
9.65  902 
9.65  927 

9.70  873 
9.70  904 
9-70  935 
9.70  966 
9.70  997 

O.29  127 
O.29  096 
0.29  065 
0.29  034 
0.29  003 

9-94  956 
9.94  949 
9-94  943 
9-94  936 
9.94  930 

55 
54 
53 
52 
5i 

10 

ii 

12 
13 
14 

9-65  952 
9.65  976 
9.66  ooi 
9.66  025 
9.66  050 

9.71  028 
9.71  059 
9.71  090 

9.71  121 

971  153 

0.28  972 
0.28  941 
0.28  910 
0.28  879 
0.28  847 

9-94  923 
9-94  9J7 
9-94  9H 
9-94  9°4 
9-94  898 

50 

49 
48 

47 
46 

15 

16 

17 
18 

19 

9.66  075 
9.66  099 
9.66  124 
9.66  148 
9.66  173 

24 
25 
24 
25 

9.71  184 
9.71  215 
9.71  246 
9.71  277 
9.71  308 

0.28  816 
0.28  785 
0.28  754 
0.28  723 
0.28  692 

9-94  891 
9-94  885 
9-94  878 
9.94  871 
9  94  865 

45 
44 
43 
42 

4i 

2O 

21 
22 
23 

24 

9.66  197 

9.66  221 
9.66  246 
9.66  270 
9.66  295 

24 
25 
24 
25 

9.71  339 
9.71  370 
9.71  401 

9.71  431 
9.71  462 

0.28  661 
0.28  630 
0.28  599 
0.28  569 
0.28  538 

9-94  858 
9-94  852 
9-94  845 
9-94  839 
9-94  832 

40 

39 
38 
37 
36 

25 
26 

27 
28 
29 

9.66  319 

9-66  343 
9.66  368 
9.66  392 
9.66  416 

24 
25 
24 
24 

9-7i  493 
9-71  524 
9-71  555 
9.71  586 
9.71  617 

0.28  507 
0.28  476 
0.28  445 
0.28  414 
0.28  383 

9.94  826 
9-94  819 
9-94  813 
9.94  806 

9-94  799 

35 
34 
33 
32 
3i 

30 

3i 
32 
33 
34 

9.66  441 
9.66  465 
9.66  489 
9.66  513 
9-66  537 

25 
24 
24 
24 
24 
25 
24 
24 
24 
24 

9.71  648 
9.71  679 
9.71  709 
9.71  740 
9.71  771 

0.28  352 
0.28  321 
0.28  291 
0.28  260 
0.28  229 

9.94  793 
9-94  786 
9.94  780 

9-94  773 
9.94  767 

30 

29 
28 
27 
26 

35 
36 
37 
38 
39 

9.66  562 
9.66  586 
9.66  610 
9.66  634 
9.66  658 

9.71  802 
9-7i  833 
9.71  863 
9.71  894 
9.71  925 

0.28  198 
0.28  167 
0.28  137 
0.28  106 
0.28  075 

9-94  76o 
9-94  753 
9-94  747 
9-94  740 
9-94  734 

25 
24 

23 

22 
21 

^O~ 

19 

18 

17 
16 

40 

4i 
42 
43 

44 

9.66  682 
9.66  706 
9.66  731 
9-66  755 
9.66  779 

24 
24 
25 
24 

24 

9-71  955 
9.71  986 
9.72  017 
9.72  048 
9.72  078 

0.28  045 
0.28  014 
0.27  983 
0.27  952 
0.27  922 

9.94  727 
9-94  720 
9-94  714 
9-94  707 
9-94  700 

45 
46 

47 

48 
49 

9.66  803 
9.66  827 
9.66  851 
9.66  875 
9.66  899 

24 
24 
24 
24 
24 

9.72  109 
9.72  140 
9.72  170 

9.72  201 
9.72  231 

0.27  891 
0.27  860 
0.27  830 
0.27  799 
0.27  769 

9-94  694 
9.94  687 
9.94  680 

9-94  674 
9.94  667 

15 
14 
13 

12 
II 

5O 

Si 

52 
53 

54 

9.66  922 
9.66  946 
9.66  970 
9.66  994 
9.67  018 

23 

24 
24 
24 
24 

9.72  262 
9-72  293 
9.72  323 

9-72  354 
9.72  384 

0.27  738 
0.27  707 
0.27  677 
0.27  646 
0.27  616 

9.94  660 
9.94  654 

9-94  647 
9.94  640 

9-94  634 

10 

9 
8 

\ 

11 

57 
58 
59 

9.67  042 
9.67  066 
9.67  090 
9.67  113 
9.67  137 

24 
.  24 
23 
24 

9-72  415 
9-72  445 
9.72  476 
9.72  506 
9-72  537 

0.27  585 
0.27  555 
0.27  524 
0.27  494 
0.27  463 

9.94  627 
9.94  620 
9-94  614 
9-94  607 
9.94  600 

5 
4 
3 

2 

I 

60 

9.67  161 

9.72  567 

0.27  433 

9-94  593 

7 

0 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.Tang. 

L.  Sin. 

d. 

/• 

Prop.  Pts. 

62< 


28< 


/• 

L.  Sin. 

d. 

L.Tang. 

c.  d. 

L.Cotg. 

L.  Cos. 

d. 

Prop.  Pts. 

0 

I 

2 

3 
4 

9.67  161 
9.67  185 
9.67  208 
9.67  232 
9.67  256 

24 

23 
24 
24 
24 
23 
24 
23 
24 
24 
23 
24 
23 
24 
23 
24 
23 
24 
23 
24 
23 
24 
23 
23 
24 
23 
23 
24 
23 
23 
24 
23 
23 
23 
23 
24 
23 
23 
23 
23 
23 
23 
23 
23 
23 
24 
23 
23 

22 

9.72  567 
9.72  598 
9.72  628 
9.72  659 
9.72  689 

31 
30 
31 
30 
31 
30 
30 
31 
3° 
31 

3° 
3° 
3i 
3<> 
30 

3i 
30 
30 
3° 
3i 
3° 
3° 
30 
30 
3i 
3° 
3° 
3° 
3° 
30 
3i 
30 
30 
30 
30 

3° 
3<> 
30 
3° 
30 
30 
3° 
3° 
i° 
3° 
30 
3° 
3° 
3° 
30 
30 
3° 
29 
30 
30 
30 
3<> 
3<> 
29 
30 

0.27  433 
0.27  402 
0.27  372 
0.27  341 
0.27  311 

9-94  593 
9-94  587 
9-94  58o 
9-94  573 
9-94  567 

6 
7 
7 
6 
7 
7 
7 
6 
7 
7 

7 
6 

7 
7 
7 

7 

6 

7 
7 
7 

7 
6 
7 
7 
7 
7 
7 
6 
7 
7 
7 
7 
7 
7 
7 
6 
7 
7 
7 
7 
7 
7 
7 
7 
7 

7 
6 
7 
7 
7 
7 
7 
7 
7 
7 
7 
7 
7 
7 

60 

59 
58 
57 
56 

6 
7 
8 
9 

10 
20 

3° 
40 

50 

] 

2 

4 
c 

*  6 

7 
8 

9 

10 
20 

30 
40 

50 

I 

2 

3 
4 
5 

3i 
3-1 
3-6 
4.1 
4-7 
5-2 
10.3 

15-5 
20.7 
25.8 

2 
6        2 

7      3 
8      3 
9      4 
o      4 
so      9 
o    14 
^o    19 
o    24 

*4 
2-4 

2.8 
3-2 

3-6 
4.0 
8.0 

12.0 

16.0 

20.0 

23 
6        2 

7      2 

8         2 

9      3 
0      3- 
o      7 

0      II. 

o    14. 
o    18 

7 

o-7 
0.8 
0.9 
i.i 

1.2 
2-3 

3-5 
4-7 
5-8 

30 
3-0 

3-5 
4.0 

4-5 
5-o 

IO.O 

15.0 

2O.O 
25.0 

9 

•9 
•4 
•9 

.8 

•7 
•5 
•3 

.2 

33 

2-3 

2.7 

I'l 

3-8 
7-7 
"•5 
15-3 
19.2 

2 

6 
9 
3 
7 
3 
o 

7 
3 

6 
0.6 
0.7 
0.8 
0.9 

I.O 
2.0 

3-0 

4.0 

5-0 

5 
6 

7 
8 

9 

9.67  280 
9.67  303 
9.67  327 
9-67  350 
9-67  374 

9.72  720 
9.72  750 
9.72  780 
9.72  8n 
9.72  841 

0.27  280 
0.27  250 

0.27  220 
0.27  189 
0.27  159 

9.94  560 
9-94  553 
9-94  546 
9-94  540 
9-94  533 

55 
54 
53 
52 
5i 

1O 

ii 

12 
13 
14 

9.67  398 
9.67  421 

9-67  445 
9.67  468 
9.67  492 

9.72  872 
9.72  902 
9.72  932 
9.72  963 
9.72  993 

0.27  128 
0.27  098 
0.27  068 
0.27  037 
O.27  OO7 

9-94  526 
9-94  519 
9-94  513 
9-94  506 
9.94  499 

5O 

49 
48 
47 
46 

li 

17 

18 
19 

9-67  515 
9-67  539 
9.67  562 
9.67  586 
9.67  609 

9.73  023 
9-73  054 
9-73  084 
9-73  "4 
9-73  144 

0.26  977 
0.26  946 
0.26  916 
0.26  886 
0.26  856 

9-94  492 
9-94  485 
9-94  479 
9-94  472 
9-94  465 

45 
44 
43 
42 

4i 

2O 

21 
29 

23 

24 

9.67  633 
9  67  656 
9.67  680 
9.67  703 
9.67  726 

9-73  175 
9-73  205 
9-73  235 
9-73  265 
9-73  295 

0.26  825 
0.26  795 
0.26  765 
0.26  735 
0.26  705 

9-94  458 
9-94  451 
9-94  445 
9-94  438 
9-94  431 

40 

39 
38 
37 
36 

25 
26 

27 
28 

29 

9.67  750 
9.67  773 
9.67  796 
9.67  820 
9.67  843 

9.73  326 
9-73  356 
9-73  386 
9-73  4i6 
9-73  446 

0.26  674 
0.26  644 
0.26  614 
0.26  584 
0.26  554 

9.94  424 
9-94  417 
9-94  4io 
9.94  404 

9-94  397 

35 
34 
33 
32 
3i 

30 

3i 
32 

33 
34 

9.67  866 
9.67  890 

9-67  913 
9.67  936 

9-67  959 

9  73  476 
9-73  5°7 
9-73  537 
9-73  567 
9-73  597 

0.26  524 
0.26  493 
0.26  463 
0.26  433 
0.26  403 

9-94  390 
9-94  383 
9-94  376 
9.94  369 
9-94  362 

30 

29 
28 
27 
26 

35 
36 
37 
38 
39 

9.67  982 
9.68  006 
9.68  029 
9.68  052 
9-68  075 

9.73  627 
9-73  657 
9-73  687 
9-73  717 
9-73747 

0.26  373 
0.26  343 
0.26  313 
0.26  283 
0.26  253 

9-94  355 
9-94  349 
9-94  342 
9-94  335 
9-94  328 

25 
24 
23 

22 
21 

40 

4i 
42 
43 

44 

9.68  098 
9.68  121 
9.68  144 
9.68  167 
9.68  190 

9-73  777 
9  73  807 
9-73  837 
9-73  867 
9-73  897 

0.26  223 
0.26  193 
0.26  163 
0.26  133 
0.26  103 

9-94  321 
9-94  3H 
9-94  307 
9.94  300 

9-94  293 

20 

19 

18 

17 
16 

45 
46 
47 
48 
49 

9.68  213 
9-68  237 
9.68  260 
9.68  283 
9.68  305 

9-73  927 
9-73  957 
9-73  987 
9.74  017 

9-74  047 

0.26  073 
0.26  043 
0.26  013 
0.25  983 
0-25  953 

9.94  286 
9-94  279 
9-94  273 
9.94  266 

9-94  259 

15 
14 
13 

12 
II 

5O 

5i 
52 
53 

54 

9.68  328 
9-68  351 
9-68  374 
9.68  397 
9.68  420 

23 
23 
23 
23 
23 
23 
23 
23 
23 
22 

23 

9-74  077 
9  74  107 
9-74  137 
9.74  166 

9-74  196 

0.25  923 
0.25  893 
0.25  863 
0.25  834 
0.25  804 

9-94  252 
9-94  245 
9-94  238 
9-94  231 
9.94  224 

10 

9 
8 

7 
6 

6 

7 
8 

9 

10 
20 

30 
40 

5° 

55 
56 
57 
58 
59 

9-68  443 
9.68  466 
9.68  489 
9.68  512 
9-68  534 

9.74  226 
9-74  256 
9.74  286 
9-74  3l6 
9-74  345 

0.25  774 
0.25  744 
0.25  714 
0.25  684 
0-25  655 

9.94  217 
9.94  210 
9-94  203 
9-94  I96 
9.94  189 

5 
4 
3 

2 

I 

60 

9-68  557 

9-74  375 

0.25  625 

9.94  182 

7 

0 

L.  Con. 

d. 

L.Cotg.  c.  d.  L.Tnng. 

L.  Sin.      d. 

/ 

Prop.  Pis. 

61 


29< 


f 

JL.  Sin. 

d. 

L.Tang.c.  d.  L.  Cotg. 

L.  Cos. 

d. 

Prop.  Pts. 

o 

I 

2 

3 

4 

9-68  557 
9.68  580 
9.68  603 
9.68  625 
9.68  648 

23 
23 

22 
23 
23 

23 
22 

23 
23 

22 

23 
22 

23 
23 

9-74  375 
9-74  405 
9-74  435 
9-74  465 
9.74  494 

30 
3° 
30 
29 
3° 
30 
29 
30 
30 
30 
29 
30 
30 
29 
3° 
3° 
29 
30 
29 
30 
29 
30 
3° 
29 
30 
29 
30 
29 
30 
29 
30 
29 
30 
29 
29 
3° 
29 
30 
29 
29 

30 
29 
3° 
29 
29 
30 
29 
29 
29 
30 

29 
29 
29 
30 
29 
29 
29 
3° 
29 

29 

0.25  625 
0-25  595 
0-25  565 
0.25  535 
0.25  506 

9.94  182 

9-94  175 
9.94  168 
9.94  161 
9-94  154 

7 
7 
7 
7 
7 
7 
7 
7 
7 
7 
7 
7 
8 
7 
7 
7 
7 
7 
7 
7 
7 
7 
7 
8 
7 
7 
7 
7 
7 
7 

7 

8 

7 
7 
7 
7 
7 
8 
7 
7 
7 
7 
8 
7 
7 

7 

8 

7 
7 
7 

7 
8 

7 

7 

60 

59 
58 
57 
56 

6 

7 
8 

9 

10 
20 
30 

30 
3-o 
3-5 
4.0 

4-5 
S-o 

10.0 

15-0 

20.0 
25.0 

29 
2.9 

3-4 
3-9 
4-4 
4.8 

9-7 
14.5 
19-3 
24.2 

23 

2-3 
2-7 
3-i 
3-5 
3-8 
7-7 
"•5 
15-3 
19.2 

22 
2.2 

2.6 
2-9 

3-3 
3-7 
7-3 

II.O 

14.7 
18.3 

8   7 
.8  0.7 
.9  0.8 
.1  0.9 

.2   I.I 

•3   L2 

•7  2.3 
•o  3-5 
•3  4-7 
•7  1  5-8 

5 
6 

7 

8 

9 

9.68  671 
9.68  694 
9.68  716 
9.68  739 
9.68  762 

9-74  524 
9-74  554 
9-74  583 
9.74  613 

9-74  643 

0.25  476 
0.25  446 
0.25  417 
0.25  387 
0.25  357 

9-94  147 
9-94  140 
9-94  133 
9.94  126 

9-94  U9 

55 
54 
53 
52 
Si 

10 

ii 

12 

13 
14 

9.68  784 
9.68  807 
9.68  829 
9.68  852 
9.68  875 

9-74  673 
9-74  702 
9-74  732 
9-74  762 
9.74  791 

0.25  327 
0.25  298 
0.25  268 
0.25  238 
0.25  209 

9.94  112 

9-94  i°5 
9.94  098 

9-94  09° 
9.94  083 

50 

49 
48 
47 
46 

40 
50 

6 
7 
8 
9 

10 

20 

3° 

40 
50 

6 

7 
8 

9 

IO 
20 
30 
'  40 

50 

6 

7 
8 

9 

10 
20 
30 
40 
50 

6  o 
7  o 
8  i 
9  i 

10  I 
20  2 

3°  4 
40  5 
50  6 

II 

17 

18 
19 

9.68  897 
9.68  920 
9.68  942 
9.68  965 
9.68  987 

23 
22 

23 
22 

23 
22 

23 
22 
23 

9.74  821 

9-74  851 
9.74  880 
9.74  910 
9-74  939 

0.25  179 
0.25  149 

0.25  120 
0.25  090 
O.25  O6  I 

9.94  076 

9-94  069 
9.94  062 

9-94  055 
9-94  048 

45 
44 
43 
42 
41 

20 

21 
22 
23 
24 

9.69  oio 
9.69  032 

9-69  055 
9.69  077 
9.69  100 

9-74  969 
9.74  998 
9-75  028 
9-75  058 
9-75  087 

0.25  031 
0.25  002 
0.24  972 
O.24  942 
0.24  913 

9.94  041 
9.94  034 
9-94  027 
9.94  020 

9-94  OI2 

40 

39 

38 

i 

25 
26 

27 
28 

29 

9.69  122 
9.69  144 
9.69  167 
9.69  189 
9.69  212 

22 

23 
22 
23 

9-75  "7 
9-75  146 
9-75  176 
9-75  205 
9-75  235 

0.24  883 
0.24  854 
0.24  824 

0.24  795 
0.24  765 

9.94  005 

9-93  998 
9-93  99i 
9-93  984 
9-93  977 

35 
34 
33 
32 
3i 

30 

3i 

32 
33 
34 

9-69  234 
9.69  256 
9.69  279 
9.69  301 
9.69  323 

22 

23 
22 
22 
22 

23 
22 
22 
22 

22 

23 
22 
22 
22 

9.75  264 
9-75  294 
9-75  323 
9-75  353 
9-75  382 

0.24  736 
0.24  706 
0.24  677 
0.24  647 
0.24  618 

9-93  970 
9-93  963 
9-93  955 
9-93  948 
9-93  94i 

30 

29 
28 

27 
26 

35 
36 
37 
38 
39 

9-69  345 
9.69  368 
9.69  390 
9.69  412 
9.69  434 

9-75  4" 
9-75  44i 
9-75  470 
9-75  500 
9-75  529 

0.24  589 

0.24  559 
0.24  530 
0.24  500 
0.24  471 

9-93  934 
9-93  927 
9-93  920 
9-93  912 
9-93  905 

25 
24 
23 

22 
21 

4O 

4i 
42 
43 
44 

9.69  456 
9.69  479 
9.69  501 
9-69  523 
9-69  545 

9-75  558 
9-75  588 
9-75  617 
9-75  647 
9-75  676 

0.24  442 
0.24  412 
0.24  383 
0.24  353 
0.24  324 

9-93  898 
9-93  891 
9-93  884 
9.93  876 
9-93  869 

»0 

*9 

18 

17 
16 

45 
46 

47 
48 
49 

9.69  567 
9.69  589 
9.69  611 
9.69  633 
9-69  655 

22 
22 
22 
22 
22 
22 
22 
22 
22 

9-75  705 
9-75  735 
9-75  764 
9-75  793 
9-75  822 

0.24  295 
0.24  265 
0.24  236 
0.24  207 
0.24  178 

9.93  862 
9-93  855 
9-93  847 
9-93  840 
9-93  833 

15 
14 
13 

12 
II 

50 

Si 

52 
53 
54 

9.69  677 
9.69  699 
9.69  721 

9-69  743 
9.69  765 

9-75  852 
9-75  881 
9-75  9io 
9-75  939 
9-75  969 

0.24  148 
0.24  119 
0.24  090 
0.24  06  1 
0.24  031 

9.93  826 
9-93  819 
9-93  8n 
9-93  804 
9-93  797 

10 

9 
8 

7 
6 

3 

57 
58 
59 

9.69  787 
9.69  809 
9-69  831 
9-69  853 
9.69  875 

22 
22 
22 
22 
22 

9-75  998 
9.76  027 
9.76  056 
9.76  086 
9.76  115 

0.24  002 

0.23  973 
0.23  944 
0.23  914 
0.23  885 

9-93  789 
9-93  782 
9-93  775 
9  93  768 
9.93  760 

7 
7 
7 

8 

5 
4 
3 

2 

I 

60 

9.69  897 

9.76  144 

0.23  856 

9-93  753 

7 

0 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.Tang. 

L.  Sin. 

d. 

r 

Prop.  Pts. 

60C 


30C 


/• 

L.  Sin. 

d. 

L.Tang.  c.  d.'  L.  Cotg. 

L.  Cos.  j  d. 

Prop.  ] 

Pts. 

o 

I 

2 

3 
4 

9.69  897 
9.69  919 
9.69  941 
9.69  963 
9.69  984 

22 
22 
22 
21 

9.76  144 
9.76  173 
9.76  202 
9.76  231 
9.76  261 

29 
29 
29 

3° 
29 

29 
29 
29 
29 
29 
29 
29 
29 
29 
29 
29 
30 
29 

29 
28 

29 
29 
29 
29 
29 
29 
29 
29 
29 
29 
29 
29 
28 
29 
29 
29 
.-29 
29 
28 
29 
29 
29 
29 
a8 
29 
29 
29 
28 
29 
29 
28 
29 
29 
29 
28 
29 
28 
29 
29 
28 

0.23  856 
0.23  827 
0.23  798 
0.23  769 
0.23  739 

9-93  753 
9-93  746 
9-93  738 
9-93  73i 

9-93  724 

7 
8 
7 
7 
7 
8 
7 
7 
8 
7 

7 

8 
7 
8 
7 

7 

8 
7 
7 
8 

7 
8 
7 
7 
8 

7 
8 
7 
8 
7 

7 

8 
7 
8 
7 
8 
7 
8 
7 
8 

7 
8 
7 
8 
7 
8 
7 
8 
7 
8 

7 
8 
7 
8 
8 

7 
8 

7 
8 
7 

GO 

59 
58 
57 
56 

3 
6   3 

7   3 
8   4 

9   A 

i°   5 

20  1C 

30  is 

4O  2C 
50   25 

6 
7 

8 

9 

10 
20 

30 
40 

50 

6 
7 
8 

9 

10 
20 

3° 

40 
50 

6 
7 
8 

9 

10 
20 

30 
40 

50 

6  c 

7  c 
8  i 

9  * 

10   I 
20  2 

3°  A 
40  5 
50  t 

o   29 
.0   2.9 

•5   3-4 
.0   3.9 

•5   4-4 
.0   4.8 
.0   9.7 
.0  14.5 
.0  19.3 
.0  24.2 

28 

2.8 

3-3 
3-7 
4.2 

4-7 
9-3 
14.0 
18.7 
23-3 

22 

2.2 
2.6 
2.9 

3-3 
3-7 
7-3 

II.O 

14.7 

18.3 

21 
2.1 

2-5 
2.8 

3-2 

3.5 

7.0 
10.5 
14.0 
17.5 

8   7 
.8  0.7 
.9  0.8 
.1  0.9 

.2   I.I 

.3  i.a 

•7  2-3 
•o  3-5 
•3  4-7 
•7  5-8 

1 

7 
8 
9 

9.70  006 
9.70  028 
9.70  050 
9.70  072 
9.70  093 

22 
22 
22 
21 
22 
22 
22 
21 
22 
22 
21 
22 
21 
22 
22 
21 
22 
21 
22 

9.76  290 
9-76  3*9 
9.76  348 
9.76  377 
9.76  406 

0.23  710 
0.23  68  1 
0.23  652 
0.23  623 
0-23  594 

9-93  717 
9-93  709 
9-93  702 
9-93  695 
9-93  687 

55 
54 
53 
52 
51 

1O 

II 

12 
13 
14 

9.70  115 
9.70  137 
9.70  159 
9.70  180 
9.70  202 

9-76  435 
9.76  464 
9-76  493 
9.76  522 
9-76  551 

0.23  565 
0.23  536 
0.23  507 
0.23  478 
0.23  449 

9.93  680 
9-93  673 
9-93  665 
9-93  658 
9-93  650 

50 

49 
48 

47 
46 

IS 

16 
17 
18 
19 

9.70  224 
9.70  245 
9.70  267 
9.70  288 
9.70  310 

9.76  580 
9.76  609 
9.76  639 
9.76  668 
9.76  697 

0.23  420 
0.23  391 
0.23  361 
0.23  332 
0.23  303 

9-93  643 
9-93  636 
9-93  628 
9-93  621 
9-93  614 

45 
44 
43 
42 
41 

20 

21 
22 

23 
24 

9.70  332 
9-70  353 
9-70  375 
9.70  396 
9.70  418 

9.76  725 
9-76  754 
9.76  783 
9.76  812 
9.76  841 

0.23  275 
0.23  246 
0.23  217 
0.23  188 
0.23  159 

9-93  606 
9-93  599 
9-93  591 
9-93  584 
9-93  577 

40 

39 
38 

11 

25 
26 

27 
28 

29 

9-7°  439 
9.70  461 
9.70  482 
9.70  504 
9-70  525 

22 
21 
22 
21 

9.76  870 
9.76  899 
9.76  928 
9-76  957 
9.76  986 

0.23  130 
0.23  101 
0.23  072 
0.23  043 
0.23  014 

9-93  569 
9-93  562 
9-93  554 
9-93  547 
9-93  539 

35 
34 
33 
32 
3i 

30 

3i 
32 
33 

34 

9-70  547 
9.70  568 
9.70  590 
9.70  611 
9.70  633 

21 
22 
21 
22 

9.77  015 
9-77  044 
9-77  073 
9.77  101 

9-77  130 

0.22  985 
0.22  956 
0.22  927 
O.22  899 
0.22  870 

9-93  532 
9-93  525 
9-93  517 
9-93  5io 
9-93  502 

30 

29 

28 
27 
26 

H 

37 
38 
39 

9.70  654 
9.70  675 
9.70  697 
9.70  718 
9.70  739 

21 
22 
21 
21 

9-77  159 
9.77  188 
9-77  217 
9.77  246 
9.77  274 

0.22  841 
O.22  8l2 
0.22  783 

0.22  754 

O.22  726 

9-93  495 
9-93  487 
9-93  48o 
9-93  472 
9-93  465 

25 
24 
23 

22 
21 

4O 

4i 
42 
43 
44 

9.70  761 
9.70  782 
9.70  803 
9.70  824 
9.70  846 

21 
21 
21 
22 

9-77  303 
9-77  332 
9-77  361 
9.77  390 
9-77  4i8 

O.22  697 

0.22  668 

O.22  639 
0.22  6lO 
O.22  582 

9-93  457 
9-93  450 
9-93  442 
9-93  435 
9-93  427 

20 

19 

18 

17 

16 

45 
46 

47 
48 

49 

9.70  867 
9.70  888 
9.70  909 
9.70  931 
9.70  952 

21 
21 
22 
21 
21 
21 
21 
21 
22 
21 
21 
21 
91 
21 
21 

9-77  447 
9-77  476 
9-77  505 
9-77  533 
9-77  562 

0.22  553 

0.22  524 

0.22  495 

0.22  467 
O.22  438 

9-93  420 
9-93  412 
9-93  405 
9-93  397 
9-93  390 

15 
14 
13 

12 
II 

50 

Si 
52 
53 
54 

9.70  973 
9.70  994 
9.71  015 
9-71  036 
9.71  058 

9-77  59i 
9-77  619 
9-77  648 
9-77  677 
9.77  706 

O.22  409 
0.22  381 
0.22  352 
0.22  323 
0.22  294 

9-93  382 
9-93  375 
9-93  367 
9-93  3°° 
9-93  352 

10 

9 

8 

7 
6 

55 
56 
57 
58 
59 

9.71  079 
9.71  100 
9.71  I2i 
9.71  142 
9-71  163 

9-77  734 
9-77  763 
9-77  791 
9  77  820 

9-77  849 

0.22  266 
0.22  237 
0.22  209 
0.22  ISO 
0.22  151 

9-93  344 
9-93  337 
9-93  329 
9.93  322 

9-93  314 

5 
4 
3 

2 
I 

60 

9.71  184 

9-77  877 

0.22  123 

9-93  3<V 

0 

1..  Cog.  i  d. 

L.  Cotg.  c.  d.  L.Taiig. 

L.  Sin.   d. 

r 

I'rop. 

Pt8. 

59' 


31 


53 


/• 

L.  Sin. 

d. 

L.Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

Pro] 

>,  Pts. 

o 

I 

2 

3 

4 

9.71  184 
9-71  205 
9.71  226 
9.71  247 
9.71  268 

21 

21 
21 

21 

9.77  877 
9-77  906 
9-77  935 
9-77  963 
9.77  992 

29 
29 
28 
29 
28 

O.22  123 
0.22  094 
O.22  065 
0.22  037 
O.22  OO8 

9-93  307 
9-93  299 
9-93  291 
9-93  284 
9.93  276 

8 
8 
7 
8 

60 

59 
58 
57 
56 

6 
7 

29 

2.9 

3.4 

5 
6 

7 
8 

9 

9.71  289 
9.71  310 
9-71  33i 
9-7i  352 
9-71  373 

21 
21 
21 
21 

9.78  020 
9.78  049 
9.78  077 

9.78  106 
9.78  135 

29 
28 
29 
29 
28 

0.21  980 
O.2I  951 
0.21  923 
O.2I  894 
0.21  865 

9.93  269 
9.93  26! 
9-93  253 
9-93  246 
9-93  238 

8 
8 
7 
8 
g 

55 
54 
53 
52 
5i 

8 
9 

10 

20 
3° 

3-9 
4-4 
4.8 

9-7 
14-5 

10 

ii 

12 
13 
14 

9-71  393 
9.71  414 

9-7i  435 
9-7i  456 
9.71  477 

21 
21 
21 
21 

9.78  163 
9.78  192 

9.78  220 
9.78  249 
9.78  277 

29 
28 
29 
28 

O.2I  837 
0.21  808 
O.2I  780 
0.21  751 
0.21  723 

9.93  230 
9-93  223 
9-93  215 
9-93  207 
9.93  200 

7 
8 
8 

7 
g 

5O 

49 
48 

47 
46 

40 
50 

19-3 
24.2 

28 

IS 

16 

17 
18 

19 

9.71  498 
9-7i  519 
9-7i  539 
9.71  560 
9.71  581 

21 
20 
21 

21 

9.78  306 

9-78  334 
9.78  363 
9.78  391 
9.78  419 

28 
29 
28 
28 

0.21  694 
0.21  666 
O.2I  637 
0.21  609 
O.2I  581 

9-93  192 
9-93  184 
9-93  177 
9.93  169 
9-93  161 

8 

7 
8 
8 

45 
44 
43 
42 
4i 

6 

7 
8 

9 

10 

2.8 

3-3 

3-7 

4-2 

4-7 

20 

21 
22 

23 
24 

9.71  602 
9.71  622 
9.71  643 
9.71  664 
9.71  685 

20 
21 
21 
21 

9.78  448 
9.78  476 
9-78  505 
9-78  533 
9.78  562 

29 
28 
29 
28 
29 

0.21  552 
0.21  524 

0.21  495 

O.2I  467 
0.21  438 

9-93  154 
9-93  X46 
9-93  138 
9-93  131 
9-93  123 

7 
8 
8 

7 

8 
g 

40 

39 

38 
37 
36 

20 

30 
40 

50 

9-3 
14.0 
18.7 
23-3 

25 
26 
27 
28 

29 

9.71  705 
9.71  726 
9.71  747 
9.71  767 
9.71  788 

21 
21 
20 
21 

9.78  590 
9.78  618 
9.78  647 
9.78  675 
9.78  704 

28 
29 
28 
29 

O.2I  4IO 
0.21  382 

0.21  353 

0.21  325 
O.2I  296 

9-93  "5 
9-93  108 
9-93  ioo 
9-93  092 
9.93  084 

7 
8 
8 
8 

35 
34 
33 
32 
3i 

6 

7 
8 

21 
2.1 

2-5 
2.8 

30 

3i 
32 

33 
34 

9.71  809 
9.71  829 
9.71  850 
9.71  870 
9.71  891 

20 
21 
20 
21 

9.78  732 
9.78  760 
9.78  789 
9.78  817 
9.78  845 

28 
29 
28 
28 

O.2I  268 
O.2I  240 
0.21  211 
0.21  183 
0.21  155 

9-93  077 
9-93  069 
9-93  061 
9-93  053 
9.93  046 

8 
8 
8 
7 

3O 

29 
28 

27 

26 

9 

10 
20 

3° 

40 

3-2 

3-5 
7.0 

10.5 
14.0 

35 
36 
37 
38 
39 

9.71  911 
9.71  932 
9-7i  952 
9-7i  973 
9.71  994 

21 
20 
21 
21 

9.78  874 
9.78  902 
9.78  930 
9-78  959 
9.78  987 

29 
28 
28 
29 
28 

0.21  126 
0.21  098 
O.2I  070 
0.21  041 
O.2I  OI3 

9-93  038 
9-93  030 

9.93  022 

9-93  014 
9-93  007 

8 
8 
8 
7 

25 
24 
23 

22 
21 

5° 
6 

*7-5 
20 

2.0 

40 

4i 
42 

43 

44 

9.72  014 
9.72  034 
9-72  055 
9.72  075 
9.72  096 

2O 
21 
2O 
21 

9.79  015 

9-79  043 
9.79  072 
9.79  100 
9.79  128 

28 
29 
28 
28 

0.20  985 

0.20  957 

0.20  928 
0.20  900 
O.2O  872 

9.92  999 
9.92  991 
9.92  983 
9.92  976 
9.92  968 

8 
8 

7 
8 

20 

19 

18 

17 
16 

7 
8 

9 

10 
20 

2-3 

2.7 

3-0 
3-3 
6-7 

45 
46 

47 
48 

49 

9.72  116 
9.72  137 
9.72  157 
9.72  177 
9.72  198 

21 
20 
2O 
21 

9-79  156 
9.79  185 
9-79  213 
9-79  24i 
9.79  269 

29 

28 
28 
28 

0.20  844 
0.20  815 
0.20  787 

0.20  759 

0.20  731 

9.92  960 
9.92  952 
9.92  944 
9.92  936 
9.92  929 

8 
8 
8 
7 

15 
14 
13 

12 
II 

40 
50 

13-3 
16.7 

50 

5i 

52 
53 
54 

9.72  218 
9.72  238 
9.72  259 
9.72  279 
9.72  299 

20 
21 
20 
2O 

9-79  297 
9-79  S26 
9-79  354 
9.79  382 
9.79  410 

29 
28 
28 
28 

O.2O  703 
O.2O  674 
O.2O  646 

0.20  618 

O.2O  590 

9.92  921 
9.92  913 
9.92  905 
9.92  897 
9.92  889 

8 
8 
8 
8 

10 

9 
8 

6 

6  c 
7  c 
8  i 

9  i 

7 
.8  0.7 
(.9  0.8 
.1  0.9 

.2  I.I 

55 
56 
57 
58 
59 

9.72  320 
9.72  340 
9.72  360 
9.72  381 
9.72  401 

2O 
2O 
21 
20 

9-79  438 
9.79  466 

9-79  495 
9-79  523 
9-79  55i 

28 
29 
28 
28 

O.2O  562 

0.20  534 

0.20  505 

0.20  477 
0.20  449 

9.92  881 
9-92  874 
9.92  866 
9.92  858 
9.92  850 

7 
8 
8 
8 

5 
4 
3 

2 

I 

2O  2 

30  A 
4«>  S 
50  6 

z.a 

•7  2.3 
•o  3-5 

•3  4-7 
•7  5-8 

60 

9.72  421 

9-79  579 

O.2O  421 

9.92  842 

0 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.Tang. 

L.  Sin. 

d. 

/• 

Proj 

.Pts. 

58( 


54 


32' 


r 

L.  Sin. 

d. 

L.Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

Ft 

op.  1 

*ts. 

0 

i 

2 

3 
4 

9.72  421 
9.72  441 
9.72  461 
9.72  482 
9.72  502 

20 
20 

21 
2O 

9-79  579 
9.79  607 

9-79  635 
9.79  663 
9-79  691 

28 
28 
28 
28 
28 

O.2O  421 

0.20  393 

O.2O  365 

0.20  337 

O.2O  309 

9.92  842 
9.92  834 
9.92  826 
9.92  818 
9.92  810 

8 
8 
8 
8 

60 

59 
58 
57 
56 

6 
7 

29 

2-9 

0  A 

28 

2.8 
o.o 

6 

7 

8 

9 

9.72  522 
9.72  542 
9-72  562 
9.72  582 
9.72  602 

20 
20 
20 
20 

9.79  719 
9-79  747 
9-79  776 
9-79  804 
9-79  832 

28 
29 
28 
28 
28 

O.2O  28l 
0.20  253 
O.2O  224 
0.20  196 

0.20  168 

9.92  803 

9-92  795 
9.92  787 
9.92  779 
9.92  771 

8 
8 
8 
8 
g 

55 
54 
53 
52 
5i 

8 

9 
10 

20 
30 

3-9 

4.4 
4.8 
9-7 

14-5 

3-7 
4.2 

4-7 
9-3 
14.0 

1O 

ii 

12 
13 
14 

9.72  622 
9.72  643 
9.72  663 
9.72  683 
9.72  703 

21 
20 
20 
2O 

9.79  860 
9.79  888 
9-79  9i6 
9-79  944 
9-79  972 

28 
28 
28 
28 
28 

O.2O  140 
O.2O  112 
0.20  084 
0.20  056 
O.2O  O28 

9.92  763 

9-92  755 
9.92  747 
9.92  739 
9.92  731 

8 
8 
8 
8 
g 

50 

49 
48 

47 
46 

40 
50 

19-3 
24.2 

a 

18.7 
23-3 

7 

II 

17 

18 
19 

9.72  723 
9-72  743 
9.72  763 
9.72  783 
9.72  803 

2O 
20 
20 
2O 

9.80  ooo 
9.80  028 
9.80  056 
9.80  084 

9.80  112 

28 
28 
28 

28 
28 

O.2O  OOO 
0.19  972 

0.19  944 
0.19  916 
0.19  888 

9.92  723 
9.92  715 
9.92  707 
9.92  699 
9.92  691 

8 
8 
8 
8 
g 

45 
44 
43 
42 

4i 

] 

6   2 

7   3 
8   3 
9   4 

[O   4 

•7 

.2 

.6 
.1 
•5 

SO 

21 
22 

23 

24 

9.72  823 
9.72  843 
9.72  863 
9.72  883 
9.72  902 

20 
20 
20 
*9 

9.80  140 

9.80  168 
9.80  195 
9.80  223 
9.80  251 

28 
27 
28 
28 
28 

0.19  860 
0.19  832 
0.19  805 
0.19  777 
0.19  749 

9.92  683 
9.92  675 
9.92  667 
9.92  659 
9.92  651 

8 
8 
8 
8 

4O 

39 
38 

| 

i 

jo   9 

*o  13 
(.0  18 
;o  22 

.0 

•5 

.0 

•5 

25 
26 
27 
28 
29 

9.72  922 
9.72  942 
9.72  962 
9.72  982 

9.73  002 

20 
20 
20 
2O 

9.80  279 
9.80  307 
9-8o  335 
9.80  363 
9.80  391 

28 
28 
28 
28 

0.19  721 
0.19  693 
0.19  665 
0.19  637 
0.19  609 

9.92  643 
9-92  635 
9.92  627 
9.92  619 
9.92  611 

8 
8 
8 
8 

35 
34 
33 
32 
3i 

6 
7 
8 

ai 

2.1 

2-5 
2.8 

20 
2.0 

2-3 
2.7 

30 

3i 
32 
33 

34 

9-73  022 

9-73  041 
9.73  061 

9-73  °8i 
9-73  ioi 

J9 

20 
20 
2O 

9.80  419 
9.80  447 
9.80  474 
9.80  502 
9.80  530 

28 
27 
28 
28 

0.19  581 

0-19  553 
0.19  526 
0.19  498 
0.19  470 

9.92  603 
9-92  595 
9.92  587 
9-92  579 
9.92  571 

8 
8 
8 
8 

3O 

29 

28 
27 
26 

9 

10 

20 

30 
40 

3-2 
3-5 
7.0 
10.5 
14.0 

3-0 
3-3 
6-7 

10.0 

J3'3 

35 
36 
37 
38 
39 

9-73  121 
9.73  140 
9-73  160 
9-73  180 
9.73  200 

19 
2O 
20 
20 

9-80  558 
9.80  586 
9.80  614 
9.80  642 
9.80  669 

28 
28 
28 
27 

0.19  442 
0.19  414 
0.19  386 
0-19  358 
0.19  331 

9-92  563 
9-92  555 
9.92  546 
9-92  538 
9-92  530 

8 
9 
8 
8 

25 
24 

23 

22 
21 

5° 

6 

J7-5 

19 
1.9 

10.7 

9 

0.9 

40 

4i 
42 

43 
44 

9-73  219 
9-73  239 
9-73  259 
9-73  278 
9-73  298 

*9 

20 
20 

19 
20 

9.80  697 
9.80  725 
9-8o  753 
9.80  781 
9.80  808 

28 
28 
28 
27 

0.19  303 
0.19  275 
0.19  247 
0.19  219 
0.19  192 

9.92  522 
9.92  514 
9.92  506 
9.92  498 
9.92  490 

8 
8 
8 
8 

2O 

19 

18 

17 
16 

7 

8 

9 

10 
20 

2.2 

2-5 
2.9 

3-2 
6.3 

I.I 

1.2 
1.4 

i-S 
3-0 

45 
46 

47 
48 
49 

9-73  3i8 
9-73  337 
9-73  357 
9-73  377 
9-73  396 

»9 
20 
20 
19 

9.80  836 
9.80  864 
9.80  892 
9.80  919 
9.80  947 

28 
28 
27 
28 

_o 

0.19  164 
0.19  136 
0.19  108 
0.19  081 
0.19  053 

9.92  482 
9-92  473 
9.92  465 
9-92  457 
9.92  449 

9 
8 
8 
8 
g 

15 
14 
13 

12 
II 

3° 

40 
50 

9-5 
12.7 
15-8 

8, 

4-5 
6.0 

7-5 

50 

Si 
52 
53 
54 

9-73  4i6 
9-73  435 
9-73  455 
9-73  474 
9-73  494 

19 
20 

19 
2O 

9.80  975 
9.81  003 
9.81  030 
9.81  058 
9.81  086 

28 
27 
28 
28 

0.19  025 
o.i  8  997 
o.i  8  970 
o.i  8  942 
0.18  914 

9.92  441 

9-92  433 
9.92  425 
9.92  416 
9.92  408 

8 
8 
9 
8 
g 

10 

9 
8 
7 
6 

6 

8 

9 
10 

0.8 
0.9 
i.i 

1.2 
I  3 

7 
0.7 
0.8 
0.9 
i.i 

I  2 

55 
56 
57 
58 
59 

9-73  513 
9-73  533 
9-73  552 
9-73  572 
9-73  59i 

J9 
20 
i9 

20 
»9 

9.81  113 
9.81  141 
9.81  169 
9.81  196 
9.81  224 

27 
28 
28 
27 
28 

QQ 

0.18  887 
o.i  8  859 
0.18  831 
o.i  8  804 
o.i  8  776 

9.92  400 
9.92  392 
9.92  384 
9.92  376 
9.92  367 

8 
8 
8 

9 

| 

5 
4 

3 

2 

I 

20 

30 
40 

50 

2.7 
4.0 

5-3 
6-7 

2-3 

3-5 
4-7 
5-8 

00 

9-73  611 

9.81  252 

o.i  8  748 

9-92  359 

0 

L.  COB. 

d. 

L.  Cotg. 

C.  d. 

I..T.-MI-. 

L.  Sin. 

d. 

f 

Pi 

op.  1 

Ms. 

57' 


33C 


55 


r 

L..  Sin. 

d. 

L.Tang.  c.  d. 

L.Cotg. 

L.  Cos. 

d. 

Prop. 

Pts. 

O 

i 

2 

3 

4 

9-73  6n 
9-73  630 
9-73  650 
9-73  669 
9-73  689 

J9 

20 

19 
2O 

19 

J9 

20 

X9 
19 

20 

T9 
19 
20 

19 

19 

20 

*9 
J9 
19 
*9 

20 

'9 

19 

'9 
J9 

20 

J9 
19 

r9 

9.81  252 
9.81  279 
9.81  307 
9-8i  335 
9.81  362 

27 
28 
28 
27 
28 
28 
27 
28 
27 
28 
28 
27 
28 
27 
28 
27 
28 
27 
28 
27 
28 
27 
28 
27 
28 
27 
28 
27 
28 
27 
28 
27 
28 
27 
27 
28 
27 
28 
27 
27 
28 
27 
28 
27 
27 
28 
27 
27 
28 
27 
27 
28 
27 
27 
27 
28 
27 
27 
27 
28 

o.i  8  748 
0.18  721 
0.18  693 
o.i  8  665 
0.18  638 

9-92  359 
9-92  35i 
9-92  343 
9-92  335 
9-92  326 

8 
8 
8 

9 

8' 

8 
8 

9 
8 
8 
8 

9 
8 
8 
9 

8 
8 
8 

9 
8 

8 

9 
8 
8 
9 
8 
8 

9 
8 
8 

9 
8 
8 

9 
8 

9 
8 
8 

9 

8 

9 
8 
8 

9 
8 

9 

8 

9 
8 

9 
8 

9 
8 

9 
8 

9 
8 

9 
8 

6O 

59 
58 
57 
56 

6 

8 
9 

10 

20 
30 

2 
'* 

' 
< 
<• 
C 
ll 
Ij 
2^ 

8   27 

5.8   2.7 
!-3   3-2 
t-7   3-6 

[.2   4.1 

\-7   4-5 
)-3   9-o 
^o  13-5 
.7  18.0 
1-3  22.5 

20 
2.0 

2-3 
2.7 

3-0 

11 

10.0 

13-3 

16.7 

19 

i-9 

2.2 

2-5 
2.9 

3-2 
6-3 
9-5 
12.7 
15-8 

18 

1.8 

2.1 
2.4 
2.7 

3-° 
6.0 
9.0 

12.0 
15-0 

9   8 
.9  0.8 
.1  0.9 

.2  I.I 

.4   1.2 

•5  i-3 
.0  2.7 

•5  4-o 
•o  5-3 
•5  6.7 

5 
6 

7 
8 
9 

9-73  708 
9-73  727 
9-73  747 
9-73  766 
9-73  785 

9.81  390 
9.81  418 
9.81  445 
9-8i  473 
9.81  500 

0.18  610 
0.18  582 
0.18  555 
0.18  527 
0.18  500 

9.92  318 
9.92  310 
9.92  302 
9.92  293 
9.92  285 

55 
54 
53 
52 
5i 

10 

II 

12 
13 

14 

9-73  805 
9-73  824 
9-73  843 
9-73  863 
9-73  882 

9.81  528 
9.81  556 
9-8i  583 
9.81  611 
9.81  638 

0.18  472 
0.18  444 
0.18  417 
0.18  389 
0.18  362 

9.92  277 
9.92  269 
9.92  260 
9.92  252 
9-92  244 

5O 

49 
48 

47 
46 

40 

5° 

15 

16 

17 
18 

19 

9-73  9°i 
9-73  921 
9-73  94° 
9-73  959 
9-73  978 

9.81  666 
9.81  693 
9.81  721 
9.81  748 
9.81  776 

0.18  334 
o.i  8  307 
o.i  8  279 
0.18  252 
o.i  8  224 

9-92  235 
9.92  227 
9.92  219 

9.92  211 
9.92  2O2 

45 
44 
43 
42 
4i 

6 

7 
8 

9 

10 

20 

21 

22 
23 
24 

9-73  997 
9.74  017 
9.74  036 
9-74  055 
9-74  074 

9.81  803 
9.81  831 
9.81  858 
9.81  886 
9.81  913 

0.18  197 
0.18  169 
o.i  8  142 
0.18  114 
0.18  087 

9.92  194 

9.92  186 
9.92  177 

9.92  169 
9.92  161 

4O 

39 
38 
37 
36 

2 

3 
4 
S 

I 

2 

3 
A 
5 

i 

2 

3 
4 

5 

6 

7 
8 

9 

10 

20 
3° 
40 

So 

O 

o 
o 
o 

6 

7 
8 

9 

0 
0 
0 
0 
0 

6 

7 
8 

9 
o 

0 
0 
0 
0 

c 

I 
I 
I 
I 
3 
4 
6 

7 

25 
26 

27 

28 

29 

9-74  093 
9-74  H3 
9.74  132 

9-74  151 
9-74  170 

9.81  941 
9.81  968 
9.81  996 
9.82  023 
9.82  051 

0.18  059 
o.i  8  032 
0.18  004 
0.17  977 
0.17  949 

9.92  152 
9.92  144 
9.92  136 
9.92  127 
9.92  119 

35 
34 
33 
32 
3i 

30 

3i 
32 

33 
34 

9.74  189 
9.74  208 
9.74  227 
9.74  246 
9-74  265 

*9 
19 
19 
19 
19 
19 
19 
J9 
19 
J9 

9.82  078 
9.82  106 
9.82  133 
9.82  161 
9.82  188 

0.17  922 
0.17  894 
0.17  867 
0.17  839 
0.17  812 

9.92  in 

9.92  IO2 
9.92  094 
9.92  086 
9.92  077 

30 

29 
28 
27 

26 

35 
36 
37 
38 
39 

9-74  284 
9-74  303 
9-74  322 
9-74  341 
9.74  360 

9.82  215 
9.82  243 
9.82  270 
9.82  298 
9.82  325 

0.17  785 
0.17  757 
0.17  73° 
0.17  702 
0.17  675 

9.92  069 
9.92  060 
9.92  052 
9.92  044 
9-92  035 

25 
•24 

23 

22 
21 

4O 

4i 
42 
43 
44 

9.74  379 
9-74  398 
9-74  417 
9-74  436 
9-74  455 

*9 
19 
T9 
T9 
19 
19 
19 
19 
19 
18 

*9 
*9 
19 
19 
19 
18 

19 
19 
19 
18 

J9 

9.82  352 
9.82  380 
9.82  407 
9-82  435 
9.82  462 

0.17  648 
0.17  620 
0.17  593 
0.17  565 
0.17538 

9.92  027 

9.92  018 
9.92  oio 
9.92  002 
9-9i  993 

2O 

19 

18 

17 
16 

45 
46 
47 
48 
49 

9-74  474 
9-74  493 
9.74  512  ' 
9-74  53i 
9-74  549 

9.82  489 
9.82  517 
9.82  544 
9.82  571 
9.82  599 

0.17511 
0.17483 
0.17  456 
0.17  429 
0.17  401 

9.91  985 
9.91  976 
9.91  968 

9-9i  959 
9.91  951 

15 
14 
13 

12 
II 

5O 

5i 
52 
53 
54 

9.74  568 

9-74  587 
9.74  606 
9-74  625 
9-74  644 

9.82  626 
9.82  653 
9.82  681 
9.82  708 
9-82  735 

0.17  374 
0.17  347 
0.17  319 
0.17  292 
0.17  265 

9.91  942 

9-9i  934 
9.91  925 
9.91  917 
9.91  908 

10 

9 
8 
7 
6 

55 
56 
57 
58 
59 

9.74  662 
9.74  68  1 
9-74  700 
9-74  719 
9-74  737 

9.82  762 
9.82  790 
9.82  817 
9.82  844 
9.82  871 

0.17  238 

O.I7  2IO 
0.17  183 
O.I7  156 
0.17  129 

9.91  900 
9.91  891 
9.91  883 
9.91  874 
9.91  866 

5 
4 
3 

2 

I 

6O 

9-74  756 

9.82  899 

0.17  ioi 

9.91  857 

9 

O 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.Tang. 

L.  Sin. 

d. 

/• 

Prop.  Pts. 

56C 


34C 


r 

L.  Sin. 

d. 

L.Tang.  c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

Prop.  Pts. 

0 

i 

2 

3 
4 

9-74  756 
9-74  775 
9-74  794 
9.74  812 

9-74  831 

19 
19 

18 

19 
19 
18 
X9 
19 
18 

*9 

18 
19 
J9 
18 

19 
18 

19 

18 

19 
18 

19 
18 

'9 
18 

J9 
18 

T9 
18 
18 
19 
18 

19 
18 
18 

9.82  899 
9.82  926 
9-82  953 
9.82  980 
9.83  008 

27 
27 
27 
28 
27 
27 
27 
28 
27 
27 
27 
27 
27 
28 
27 
27 
27 
27 
27 
27 
28 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
28 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
27 
26 

27 
27 
27 
27 
27 
27 
27 
27 
27 

0.17  101 
0.17  074 
0.17  047 

0.17  020 

0.16  992 

9.91  857 
9.91  849 
9.91  840 
9.91  832 
9.91  823 

8 

9 
8 

9 
g 

60 

59 
58 

1 

2 
6   2 

7   3 
8   3 
9   4 
10   4 
20   9 
30  14 
40  18 
50  23 

6 

7 
8 

9 

10 

20 

3° 
40 

50 

6 
7 
8 

9 

10 
20 
30 
40 
50 

6 

7 
8 

9 

10 

20 

3° 

40 
.  50 

6  c 
7  i 
8  i 

9  * 

10  I 
20  3 

3°  4 
40  6 

50  7 

3   37 
.8   2.7 
•3   3-2 
-7   3-6 

.2   4.1 

•7   4-5 
•3   9-° 
•o  13-5 
.7  18.0 
•3  22.5 

26 

2.6 

3-o 
3-5 
3-9 
4-3 
8-7 
13.0 

17-3 
21.7 

19 
i-9 

2.2 

2-5 
2.9 

i',2 

9-5 
12.7 
15-8 

18 
1.8 

2.1 
2.4 
2.7 

3-o 
6.0 
9.0 

12.  0 
15-0 

9   8 

.9  0.8 
.1  0.9 

.2   I.I 
.4  1.2 

•5  1-3 
.0  2.7 

•5  4-0 
•o  5-3 
•5  6.7 

5 
6 

7 
8 
9 

9-74  850 
9.74  868 
9-74  887 
9-74  9°6 
9-74  924 

9-83  035 
9.83  062 
9.83  089 
9.83  117 
9.83  144 

0.16  965 
0.16  938 
0.16  911 
0.16  883 
0.16  856 

9.91  815 
9.91  806 
9.91  798 
9.91  789 
9.91  781 

9 
8 

9 

8 

55 
54 
53 
52 
5i 

1O 

II 

12 
13 

14 

9-74  943 
9-74  96i 
9-74  98o 
9-74  999 
9-75  oi7 

9.83  171 
9.83  198 
9.83  225 
9.83  252 
9.83  280 

0.16  829 
0.16  802 
0.16  775 
o.i  6  748 
o.i  6  720 

9.91  772 
9.91  763 

9-9i  755 
9.91  746 
9.91  738 

9 
8 

9 
8 

9 

9 
8 

9 
8 

9 

9 
8 

9 
9 
8 

9 
9 
8 

9 
9 
8 
9 
9 
8 

9 
9 
9 
8 

9 
9 
8 
9 
9 
9 
8 

9 
9 
9 

9 
g 

5O 

49 
48 

47 
46 

IS 

16 

17 
18 

19 

9-75  036 
9-75  054 
9-75  073 
9-75  091 
9-75  no 

9-83  307 
9-83  334 
9.83  361 
9.83  388 
9-83  415 

0.16  693 
0.16  666 
0.16  639 
0.16  612 
0.16  585 

9.91  729 
9.91  720 
9.91  712 
9.91  703 
9.91  695 

45 
44 
43 
42 
41 

2O 

21 
22 

23 
24 

9-75  128 
9-75  147 
9-75  165 
9-75  184 
9-75  202 

9.83  442 
9.83  470 
9-83  497 
9-83  524 
9-83  55i 

0.16  558 
0.16  530 
o.i  6  503 
o.i  6  476 
0.16  449 

9.91  686 
9.91  677 
9.91  669 
9.91  660 
9.91  651 

40 

39 
38 

P 

25 
26 

27 

28 
29 

9-75  221 
9-75  239 
9-75  258 
9-75  276 
9-75  294 

9-83  578 
9.83  605 
9.83  632 

9-83  659 
9.83  686 

0.16  422 
0.16  395 
0.16  368 
0.16  341 
0.16  314 

9.91  643 
9.91  634 
9.91  625 
9.91  617 
9.91  608 

35 
34 
33 
32 
3i 

30 

3i 
32 
33 

34 

9-75  313 
9-75  33i 
9-75  350 
9-75  368 
9-75  386 

9-83  713 
9.83  740 
9-83  768 
9-83  795 
9.83  822 

0.16  287 
o.i  6  260 
0.16  232 
0.16  205 
0.16  178 

9-91  599 
9.91  591 
9.91  582 
9-91  573 
9-9i  565 

30 

29 
28 

27 
26 

35 
36 
37 
38 
39 

9-75  405 
9-75  423 
9-75  44i 
9-75  459 
9-75  478 

T9 
18 
18 
18 

J9 
18 

18 

*9 
18 
18 
18 
18 
19 

•a 

18 
18 
18 
18 

19 
18 

18 

18 
18 
18 
18 
18 

9.83  849 
9.83  876 
9-83  903 
9-83  930 
9-83  957 

0.16  151 
0.16  124 
0.16  097 
o.i  6  070 
0.16  043 

9-9i  556 
9-9i  547 
9-9i  538 
9-9i  530 
9.91  521 

25 
24 
23 

22 
21 

40 

4i 
42 
43 
44 

9-75  496 
9-75  514 
9-75  533 
9-75  55i 
9-75  569 

9.83  984 
9.84  on 
9.84  038 
9-84  065 
9.84  092 

0.16  016 
0.15  989 
0.15  962 

0.15  935 
0.15  908 

9.91  512 
9.91  504 

9-9i  495 
9.91  486 
9.91  477 

20 

19 
18 

17 
16 

45 
46 
47 
48 

49 

9-75  587 
9-75  605 
9-75  624 
9-75  642 
9-75  660 

9.84  119 
9.84  146 
9.84  173 

9.84  200 
9.84  227 

0.15  881 

0-15  854 
0.15  827 
0.15  800 
0.15  773 

9.91  469 
9.91  460 

9-9i  451 
9.91  442 

9.9i  433 

15 
14 
13 

12 
II 

50 

5i 
52 
53 
54 

9-75  678 
9-75  696 
9-75  7H 
9-75  733 
9-75  751 

9.84  254 
9.84  280 
9.84  307 

9-84  334 
9.84  361 

0.15  746 
0.15  720 
0.15693 
0.15  666 
0.15  639 

9-9i  425 
9.91  416 
9.91  407 
9.91  398 

9.91  389 

9 
9 
9 

9 
g 

10 

9 
8 
7 
6 

55 
56 
57 
58 
59 

9-75  769 
9-75  787 
9-75  805 
9-75  823 
9-75  841 

9.84  388 
9.84  415 
9.84  442 
9.84  469 
9.84  496 

0.15  612 
0.15  585 
0.15  558 
0.15  531 
0.15  504 

9.91  381 
9.91  372 
9-9i  363 
9-9i  354 
9-9i  345 

9 
9 
9 
9 

5 
4 
3 

2 
I 

GO 

9-75  859 

9-84  523 

0.15  477 

9-9i  336 

0 

L.  <  os. 

d. 

L*Cotff. 

c.  d. 

L.TniiK. 

L.  Sin.   d. 

/• 

Prop.  1 

'ts. 

55C 


35C 


57 


" 

L.  Sin. 

d. 

L.Tang. 

c.  d. 

JL.  Cotg. 

L.  Cos. 

d. 

Prop 

.  Pt«. 

0 

I 

2 

3 
4 

9-75  859 
9-75  877 
9-75  895 
9-75  9J3 
9-75  93i 

18 
18 
18 
18 

9-84  523 
9-84  55o 
9.84  576 
9.84  603 
9.84  630 

27 

26 
27 
27 

0.15  477 
0.15  450 
0.15  424 
0.15  397 
0.15  370 

9.91  336 
9-91  328 
9.91  319 
9.91  310 
9.91  301 

8 
9 
9 
9 

60 

59 
58 
57 
56 

2 
6        2 

7      3 

7       a6 
.7      2.6 

•  2        3.O 

5 
6 

7 

8 

9 

9-75  949 
9-75  967 
9-75  985 
9.76  003 
9.76  021 

18 
18 
18 
18 

9.84  657 
9.84  684 
9.84  711 
9.84  738 
9.84  764 

27 
27 
27 
27 
26 

0.15  343 
0.15  316 
0.15  289 
0.15  262 
0.15  236 

9.91  292 
9-91  283 
9  9i  274 
9.91  266 
9.91  257 

9 
9 
9 
8 
9 

55 
54 
53 
52 

8      3 
9      4 
10      4 
20      9 
3°    J3 

•6      3-5 
•i      3-9 
•5      4-3 
.0      8.7 

•5    13-0 

1O 

ii 

12 

13 

14 

9.76  039 
9.76  057 
9.76  075 
9.76  093 
9.76  in 

18 
18 
18 
18 

9.84  791 
9.84  818 
9.84  845 
9.84  872 
9.84  899 

27 
27 
27 
27 
27 

0.15  209 
0.15  182 

0.15  155 
0.15  128 
0.15  101 

9.91  248 
9.91  239 
9.91  230 

9.91  221 
9.9!  212 

9 
9 
9 
9 

50 

49 
48 

47 
46 

40    18 

50     22 

.0    17.3 
•5    21.7 

18 

15 

16 

17 
18 

19 

9.76  129 
9.76  146 
9.76  164 
9.76  182 

9.76  200 

17 
18 
18 
18 

9.84  925 
9.84  952 
9.84  979 
9.85  006 
9-85  033 

27 
27 
27 
27 
26 

0.15  075 
0.15  048 

0.15  021 

0.14  994 
0.14  967 

9.91  203 
9.91  194 
9.91  185 
9.91  176 
9.91  167 

9 
9 
9 
9 
9 

45 
44 
43 
42 

6 

7 
8 

9 

10 

1.8 

2.1 

2-4 
2.7 

21 
22 

23 

24 

9.76  218 

9.76  236 
9.76  253 
9.76  271 
9.76  289 

18 

18 

18 

9-85  059 
9.85  086 

9-85  "3 
9.85  140 
9.85  166 

27 
27 
27 
26 

0.14  941 
0.14  914 
0.14  887 
0.14  860 
0.14  834 

9.91  158 
9.91  149 
9.91  141 
9.9I  132 
9.91  123 

9 
8 

9 
9 

40 

39 
38 
37 
36 

20 
30 
40 
50 

6.0 
9.0 

12.0 
15.0 

25 
26 

27 

28 

29 

9.76  307 
9.76  324 
9.76  342 
9.76  360 
9.76  378 

17 
18 
18 

18 

9-85  193 

9.85  220 
9.85  247 

9-85  273 
9.85  300 

27 
27 
26 
27 

0.14  807 
0.14  780 

0.14  753 
0.14  727 
0.14  700 

9.91  114 
9.91!  IO5 
9.91  096 
9.91  087 
9.91  078 

9 
9 
9 
9 

35 
34 
33 
32 

•  6 

7 
8 

17 

1-7 

2.O 
2-3 

30 

32 
33 
34 

9-76  395 
9.76  413 
9.76  431 
9.76  448 
9.76  466 

17 
18 

18 

i? 
18 

9-85  327 

9-85  354 
9.85  380 
9.85  407 
9-85  434 

27 
27 
26 
27 
27 
26 

0.14  673 
0.14  646 
0.14  620 

0.14  593 
0.14  566 

9.91  069 
9.91  060 
9.91  051 
9.91  042 
9.91  033 

9 
9 
9 
9 

30 

29 
28 
27 
26 

9 
10 

20 
30 
40 
tn 

2.6 
2.8 

5.7 

8-5 
".3 

14  2 

It 

37 
38 
39 

9.76  484 
9.76  501  . 
9.76  519 
9-76  537 
9-76  554 

17 
18 
18 
17 

9.85  460 
9.85  487 
9-85  5H 
9-85  540 
9-85  567 

27 
27 
26 
27 

0.14  540 

0.14513 
0.14  486 
0.14  460 
0.14  433 

9.91  023 
9.91  014 
9.91  005 
9.90  996 
9.90  987 

9 
9 
9 
9 

25 
24 
23 

22 
21 

6 

10 
1.0 

4O 

42 
43 
44 

9-76  57? 
9.76  590 
9.76  607 
9.76  625 
9.76  642 

18 

18 
17 

9-85  594 
9.85  620 
9.85  647 
9.85  674 
9.85  700 

27 
26 
27 
27 
26 

0.14  406 
0.14  380 

0.14  353 
0.14  326 
0.14  300 

9.90  978 
9.90  969 
9.90  960 
9.90  951 
9.90  942 

9 
9 
9 
9 

20 

19 
18 

17 

16 

8 
9 

10 

20 
qo 

1.2 

3-3 

c  o 

45 
46 
47 
48 

49 

9.76  660 
9.76  677 
9.76  695 
9.76  712 
9.76  730 

17 

18 

17 
18 

9.85  727 
9-85  754 
9-85  78o 
9.85  807 
9-85  834 

27 

27 
26 

27 
27 

0.14  273 
0.14  246 

0.14  220 
0.14  193 

0.14  166 

9-9°  933 
9.90  924 
9.90  915 
9.90  906 
9.90  896 

9 
9 
9 
10 

15 
14 
13 

12 
II 

40 
50 

6.7 
8-3 

90 

5O 

52 
53 
54 

9.76  747 
9.76  765 
9.76  782 
9.76  800 
9.76  817 

18 

17 
18 
17 

9.85  860 
9.85  887 

9-85  913 
9.85  940 
9.85  967 

27 
26 

27 
27 

-£ 

0.14  140 
0.14  113 
0.14  087 
0.14  060 
0.14  033 

9.90  887 
9.90  878 
9.90  869 
9.90  860 
9.90  85! 

9 
9 
9 
9 

10 

9 
8 

7 
6 

6    o 

7    i 
8    I 

9    i 

IO     I 

.9    0.8 
.1    0.9 

.2     I.I 

.4      1.2 

5    *  3 

55 
56 
57 
58 
59 

9.76  835 
9.76  852 
9.76  870 
9.76  887 
9.76  904 

17 
18 
17 
17 

9-85  993 
9.86  020 
9.86  046 
9.86  073 
9.86  100 

27 
26 

27 
27 

0.14  007 
0.13  980 

0.13  954 
0.13  927 
0.13  900 

9.90  842 
9.90  832 
9.90  823 
9.90  814 
9.90  805 

10 
9 
9 
9 

5 
4 
3 

2 

I 

20    3 
30    4 

40    o 
50    7 

.0    2.7 
•5    4-0 
•o    5-3 
•5    6.7 

60 

9.76  922 

9.86  126 

0.13  874 

9.90  796 

9 

O 

L.  Cos. 

d. 

L.  Cotg. 

c.  d. 

L.Tang. 

L.  Sin. 

d. 

' 

Prop 

.  Pts. 

54C 


36C 


/ 

L.  Sin. 

d. 

L.Tang. 

c.  d.|  L.Cotg. 

L.  Cos. 

d. 

Prop.  Pts.  , 

0 

I 

2 

3 

4 

9.76  922 
9.76  939 
9-76  957 
9.76  974 
9.76  991 

17 
18 
17 
17 
18 

17 
18 
17 
'7 

18 
'7 
17 

9.86  126 
9.86  153 
9.86  179 
9.86  206 
9.86  232 

27 
26 
27 
26 
27 
26 
27 
26 
27 
27 
26 
27 
26 
27 
26 
27 
26 
26 
27 
26 
27 
26 
27 
26 
27 
26 
27 
26 
26 
27 
26 
27 
26 
27 
26 
26 
27 
26 
26 
27 
26 
27 
26 
26 
27 
26 
26 
27 
26 
26 
27 
26 
26 
27 
26 
26 
27 
•6 
26 
26 

0.13  874 
0.13  847 
0.13  821 
0.13  794 
0.13  768 

9.90  796 
9.90  787 
9.90  777 
9.90  768 
9-9°  759 

9 

10 

9 
9 
9 
9 

10 

9 
9 
9 

10 

9 
9 
9 

10 

9 
9 
9 

10 

9 
9 

10 

9 
9 
9 

10 

9 
9 

10 

9 
9 

10 

9 
10 

9 

9 
10 

9 
9 

10 

9 
10 

9 

10 

9 

9 
10 

9 

10 

9 

10 

9 
10 

9 

10 

9 
10 

9 
10 

9 

60 

59 
58 
57 
56 

2 
6    2 

7   3 
8   3 
9   4 
10   4 

20   C 
30  13 

40  18 

50  22 
6 

7 
8 

9 

10 
20 

3° 

40 
5° 

6 

7 
8 

9 

10 

20 

30 
40 

50 

6 

7 
8 

9 

10 
20 
30 
40 
50 

6  i 

7  3 
8  i 

9  i 

10   I 

20  3 
30  5 
40  6 

50  -a 

1 
•7 

.2 

26 

2.6 
3.O 

6 
7 
8 
9 

9.77  009 
9.77  026 

9-77  043 
9.77  061 
9.77  078 

9.86  259 
9.86  285 
9.86  312 
9.86  338 
9.86  365 

0.13  741 

0.13  715 
0.13  688 
0.13  662 
0.13  635 

9.90  750 
9.90  741 
9.90  731 
9.90  722 
9.90  713 

55 
54 
53 
52 

•6   i-5 
•i   3-9 
•5   4-3 
.0   8.7 
•5  13-0 
.0  17.3 
•5  21.7 

18 

1.8 

2.1 
2.4 
2.7 

3-° 
6.0 
9.0 

12.0 
15-0 

17 
2.0 

2-3 

2.6 
2.8 

5-7 
8-5 
"•3 
14.2 

16 
1.6 
1-9 

2.1 
2.4 
2-7 
5-3 

8.0 
10.7 
13-3 

10   9 
.0  0.9 

.2   I.I 
•3   1-2 

•5  1-4 
•7  i-5 
•3  3-° 
•o  4-5 
.7  6.0 

•3  7-5 

1O 

ii 

12 
13 

14 

9-77  095 
9.77  112 
9.77  130 
9-77  147 
9-77  164 

9-86  392 
9.86  418 
9-86  445 
9.86  471 
9.86  498 

0.13  608 
0.13  582 

0.13  555 
0.13  529 
0.13  502 

9.90  704 
9.90  694 
9.90  685 
9.90  676 
9.90  667 

5O 

49 

48 
47 
46 

15 

16 

17 

18 

19 

9.77  181 
9.77  199 
9.77  216 
9-77  233 
9-77  250 

18 
'7 
17 
17 

18 

17 
17 

9-86  524 
9.86  551 
9.86  577 
9.86  603 
9.86  630 

0.13  476 
0.13  449 
0.13  423 
0.13  397 
0.13  370 

9.90  657 
9.90  648 
9.90  639 
9.90  630 
9.90  620 

45 
44 
43 
42 

20 

21 
22 

23 
24 

9.77  268 
9-77  285 
9-77  302 
9-77  319 
9-77  336 

9.86  656 
9.86  683 
9.86  709 
9.86  736 
9.86  762 

0.13  344 
0.13  317 
0.13  291 
0.13  264 
0.13  238 

9.90  611 
9.90  602 
9.90  592 

9-90  583 
9.90  574 

40 

39 

38 

11 

25 
26 
27 
28 
29 

9-77  353 
9-77  370 
9-77  387 
9-77  405 
9-77  422 

I7 
17 

18 
17 

9.86  789 
9.86  815 
9.86  842 
9.86  868 
9.86  894 

O.I3  211 
0.13  185 
0.13  158 
0.13  132 

0.13  106 

9-9°  565 
9-9°  555 
9.90  546 

9-90  537 
9.90  527 

35 
34 
33 
32 

30 

31 

32 
33 
34 

9-77  439 
9-77  456 
9-77  473 
9-77  49° 
9-77  5°7 

17 
17 

17 

17 
17 

17 

17 
17 
17 

16 
17 

17 
17 
16 

>7 
»7 

16 

9.86  921 
9.86  947 
9.86  974 
9.87  ooo 
9.87  027 

0.13  079 
0.13  053 
0.13  026 
0.13  ooo 
0.12  973 

9.90  518 
9.90  509 
9.90  499 
9.90  490 
9.90  480 

30 

29 
28 
27 
26 

35 
36 
37 
38 
39 

9-77  524 
9-77  541 
9-77  558 
9-77  575 
9-77  592 

9-87  053 
9.87  079 
9.87  106 
9.87  132 
9.87  158 

0.12  947 

O.I2  921 
0.12  894 

0.12  868 

0.12  842 

9.90  471 
9.90  462 
9.90  452 
9.90  443 
9-9°  434 

25 
24 

23 

22 

21 

40 

42 
43 
44 

9-77  609 
9.77  626 
9-77  643 
9.77  660 
9-77  677 

9.87  185 

9.87  211 
9.87  238 
9.87  264 
9.87  290 

0.12  815 
0.12  789 
0.12  762 
0.12  736 
0.12  710 

9.90  424 
9.90  415 
9.90  405 
9.90  396 
9.90  386 

20 

19 
18 

17 
16 

47 
48 
49 

9.77  694 
9-77  7ii 
9-77  728 
9-77  744 
9-77  76i 

9.87  317 

9-87  343 
9-87  369 
9.87  396 
9.87  422 

0.12  683 
0.12  657 
0.12  631 
O.I  2  604 
0.12  578 

9.90  377 
9.90  368 
9-9°  358 
9.90  349 
9-90  339 

15 
14 
13 

12 

II 

5O 

51 
52 
53 
54 

9.77  778 
9-77  795 
9.77  812 
9-77  829 
9-77  846 

9.87  448 
9-87  475 
9.87  501 
9.87  527 
9-87  554 

0.12  552 
0.12  525 

0.12  499 
0.12  473 

0.12  446 

9.90  330 
9.90  320 
9.90311 
9.90  301 
9.90  292 

10 

9 

8 

7 
6 

55 
56 
57 
58 
59 

9.77  862 
9-77  879 
9-77  896 
9-77  913 
9-77  930 

9.87  580 
9.87  606 
9-87  633 
9.87  659 
9.87  685 

0.12  420 

0.12  394 

0.12  367 
0.12  341 
0.12  315 

9.90  282 
9.90  273 
9.90  263 
9.90  254 
9.90  244 

5 
4 
3 

2 
I 

9-77  946 

9.87  711 

0.12  289 

9-90  235 

0 

L.  COB.   d. 

L.  Cotg.  c.  d.  L.Tang. 

L.  Sin.   d. 

f 

Prop.  I'IN. 

53C 


37< 


59 


r 

L.  Sin. 

d. 

L.Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

Prop.  Pts. 

0 

i 

2 

3 

4 

9-77  946 
9-77  963 
9-77  98o 
9-77  997 
9.78  013 

17 
17 

*7 
16 

9.87  711 
9.87  738 
9.87  764 
9.87  790 
9.87  817 

27 
26 
26 
27 
26 
26 
26 
27 
26 
26 
26 
27 
26 
26 
26 
26 
27 
26 
26 
26 
26 
27 
26 
26 
26 
26 
27 
26 
26 
26 
26 
26 
27 
26 
26 
26 
26 
26 
26 
26 
27 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
27 
26 
26 
26 
26 
26 
26 
26 
26 

O.I2  289 
0.12  262 
O.I  2  236 
0.12  210 
0.12  183 

9-90  235 
9-90  225 
9.90  216 
9.90  206 
9.90  197 

10 

9 

10 

9 

60 

59 
58 
57 
56 

6 

7 
8 

9 

10 
20 

3° 

40 
50 

6 

7 
8 

9 

10 

20 

30 
40 

50 

6 

7 
8 

9 

10 
20 

30 
40 

50 

6 

7 
8 

9 

10 
20 
30 
40 
50 

27 

2.7 
3-2 
3-6 
4.1 

4-5 
9.0 

13-5 
18.0 
22.5 

26 

2.6 

3-0 
3-? 
3-9 
4-3 
8.7 
13-0 
17-3 
21.7 

17 
1-7 

2.0 

2-3 
2.6 
2.8 

5-7 
8-5 
"•3 
14.2 

16 
1.6 
1.9 

2.1 
2.4 
2.7 

5-3 
8.0 
10.7 
13-3 

io   9 

.0  0.9 

.2  I.I 

•3  1.2 

•5  1-4 
•7  S  i.S 
1-3  3-0 
>.o  4-5 
>.7  6.0 
•3  7-5 

i 

7 
8 

9 

9.78  030 
9.78  047 
9.78  063 
9.78  080 
9.78  097 

*7 
i? 
16 
17 
i? 
16 

9.87  843 
9.87  869 
9.87  895 
9.87  922 
9.87  948 

0.12  157 
0.12  131 
0.12  lOg 
0.12  078 
0.12  052 

9.90  187 
9.90  178 
9.90  168 
9.90  159 
9.90  149 

9 

IO 

9 

10 
IO 

9 

10 

9 

10 
10 

9 

10 

9 

10 
10 

9 

10 

10 

9 

10 
IO 

9 

10 

10 

9 

10 
IO 

9 

10 
IO 
10 

,9 

10 
10 
10 

9 

10 
10 
10 

9 

IO 
10 
10 
10 

9 

10 
10 
10 
10 
IO 

9 

10 
10 
IO 
IO 

55 
54 
53 
52 
5i 

IO 

ii 

12 
13 
14 

9.78  113 
9.78  130 
9.78  147 
9.78  163 
9.78  180 

17 
i? 
16 
17 

9.87  974 
9.88  ooo 
9.88  027 
9.88  053 

9.88  079 

O.I  2  O26 
0.12  000 

o.i  i  973 
o.i  i  947 
o.ii  921 

9.90  139 
9.90  130 

9.90  120 
9.90  III 

9.90  ioi 

50 

49 
48 
47 
46 

15 

16 

17 

18 

19 

9.78  197 
9.78  213 
9.78  230 
9.78  246 
9.78  263 

16 
17 
16 
X7 

9.88  105 
9.88  131 
9.88  158 
9.88  184 

9.88  210 

o.i  i  895 
o.ii  869 
o.ii  842 
o.ii  816 
o.ii  790 

9.90  091 
9.90  O82 
9.90  072 
9.90  063 
9.90  053 

45 
44 
43 
42 

41 

2O 

21 
22 

23 

24 

9.78  280 
9.78  296 
9-78  313 
9.78  329 
9.78  346 

16 

i? 

16 

17 
16 

9.88  236 
9.88  262 
9-88  289 

9-88  315 
9.88  341 

o.ii  764 
o.ii  738 
o.ii  711 
o.ii  685 
o.ii  659 

9.90  043 
9.90  034 
9.90  O24 
9.90  014 
9.90  005 

40 

39 
38 
37 
36 

25 
26 
27 
28 
29 

9.78  362 
9-78  379 
9-78  395 
9.78  412 
9.78  428 

17 

16 

17 
16 

9.88  367 
9-88  393 
9.88  420 
9.88  446 
9.88  472 

o.ii  633 
o.ii  607 
o.ii  580 
o.ii  554 
o.ii  528 

9.89  995 
9.89  985 
9.89  976 
9.89  966 
9.89  956 

35 
34 
33 
S2 
3i 

3O 

3i 
32 
33 
34 

9-78  445 
9.78  461 
9.78  478 
9.78  494 
9.78  510 

J7 

16 

17 
16 
16 

9.88  498 
9.88  524 
9-88  550 
9-88  577 
9.88  603 

o.ii  502 
o.ii  476 
o.ii  450 
o.ii  423 
o.ii  397 

9.89  947 

9-89  937 
9.89  927 
9.89  918 
9.89  908 

30 

29 
28 
27 
26 

35 
36 
37 
38 
39 

9.78  527 
9-78  543 
9.78  560 
9.78  576 
9.78  592 

16 
17 
16 
16 

9.88  629 
9.88  655 
9.88  681 
9.88  707 
9-88  733 

o.ii  371 
o.ii  345 
o.ii  319 
o.ii  293 
o.ii  267 

9.89  898 
9.89  888 
9.89  879 
9.89  869 
9.89  859 

25 
24 

23 

22 
21 

40 

41 
42 
43 
44 

9.78  609 
9.78  625 
9.78  642 
9.78  658 
9.78  674 

16 
17 
16 
16 

9-88  759 
9.88  786 
9.88  812 
9.88  838 
9.88  864 

o.ii  241 
o.ii  214 
o.ii  188 
o.ii  162 
o.ii  136 

9.89  849 
9.89  840 
9.89  830 
9.89  820 
9.89  810 

20 

19 

18 

17 

16 

45 
46 

47 
48 
49 

9.78  691 
9.78  707 
9.78  723 
9-78  739 
9.78  756 

I7 
16 
16 
16 

17 
16 

16 

i? 
16 
16 
16 
16 

J7 
16 
16 
16 

9.88  890 
9.88  916 
9.88  942 
9.88  968 
9.88  994 

O.II  IIO 

o.n  084 
o.n  058 
o.n  032 
o.n  006 

9.89  801 
9.89  791 
9.89  781 
9.89  771 
9.89  761 

15 
14 
13 

12 

II 

50 

5i 
52 
53 
54 

9.78  772 
9.78  788 
9.78  805 
9.78  821 
9.78  837 

9.89  020 
9.89  046 
9.89  073 
9.89  099 
9.89  125 

o.io  980 
o.io  954 
o.io  927 
o.io  901 
o.io  875 

9.89  752 
9.89  742 
9.89  732 
9.89  722 
9.89  712 

10 

9 

8 

6 

6  ] 

7   3 

8  ] 

9  J 

IO  ] 

55 
56 
57 
58 
59 

9-78  853 
9.78  869 
9.78  886 
9.78  902 
9.78  918 

9.89  151 
9.89  177 
9.89  203 
9.89  229 
9-89  255 

o.io  849 
o.io  823 
o.io  797 
o.io  771 
o.io  745 

9.89  702 
9.89  693 
9.89  683 
9.89  673 
9.89  663 

5 
4 
3 

2 

I 

20  I 

30  f 

40  < 

50  J 

GO 

9-78  934 

9.89  281 

o.io  719 

9-89  653 

0 

L.  Cos. 

d. 

L,.  Cotg. 

c.  d. 

L.Tang. 

JL.  Sin. 

d. 

f 

Prop.  Pts. 

52< 


6o 


38< 


r 

L.  Sin. 

d. 

L.  Tang. 

c.  d. 

JL.  Cotg. 

L.  Cos. 

d. 

Pi 

•oi 

>. 

Pts. 

O 

i 

2 

3 

4 

9-78  934 
9.78  950 
9.78  967 
9.78  983 
9.78  999 

16 

*7 
16 
16 
16 

9.89  281 
9.89  307 
9-89  333 
9-89  359 
9-89  385 

26 
26 
26 
26 

26 

o.io  719 
o.io  693 
o.io  667 
o.io  641 
o.io  615  . 

9-89  653 
9.89  643 

9-89  633 
9.89  624 
9.89  614 

IO 
10 

9 

10 

60 

59 

58 

57 

56 

6 
7 

2 
2 

J 

5 
.6 
.0 

25 

2-5 
2.9 

5 
6 

7 
8 

9 

9-79  oi5 
9-79  031 
9-79  047 
9-79  063 
9.79  079 

16 
16 
16 
16 

16 

9.89  411 

9-89  437 
9.89  463 
9.89  489 
9-89  515 

26 
26 
26 
26 
26 

o.io  589 
o.io  563 
o.io  537 
o.io  511 
o.io  485 

9.89  604 

9-89  594 
9.89  584 

9-89  574 
9.89  564 

10 
IO 
IO 
10 

55 
54 
53 
52 
51 

8 

9 

10 

20 
3° 

3 
3 
4 
8 

.'3 

•5 

•9 
•3 
•7 

.0 

3-3 
3-8 
4.2 
8-3 
12.5 

10 

ii 

12 
13 
14 

9-79  095 
9.79  in 
9.79  128 
9-79  144 
9.79  160 

16 

J7 
16 
16 
16 

9.89  541 
9.89  567 

9-89  593 
9.89  619 
9.89  645 

26 
26 
26 
26 
26 

o.io  459 
o.io  433 
o.io  407 
o.io  381 
o-io  355 

9-89  554 
9.89  544 

9-89  534 
9.89  524 
9.89  514 

IO 
IO 
10 
10 

50 

49 

48 

47 
46 

40 
50 

17 

21 

•3 
•7 

i 

16.7 

20.8 

7 

15 

16 

17 
18 

19 

9.79  176 
9-79  192 
9.79  208 
9-79  224 
9.79  240 

16 
16 
16 
16 
16 

9.89  671 
9.89  697 
9.89  723 
9.89  749 
9-89  775 

26 
26 
26 
26 

26 

o.io  329 
o.io  303 
o.io  277 
o.io  251 
o.io  225 

9.89  504 

9-89  495 
9.89  485 

9-89  475 
9.89  465 

9 

10 
10 
IO 

45 
44 
43 
42 

4i 

] 

6 

7 
8 

9 

to 

2 
2 

2 
2 

•7 
.0 

:! 

.8 

2O 

21 
22 
23 
24 

9-79  256 
9-79  272 
9.79  288 
9-79  304 
9-79  319 

16 
16 
16 
15 

rfi 

9.89  801 
9.89  827 
9-89  853 
9-89  879 
9.89  905 

26 
26 
26 
26 
ifi 

o.io  199 
o.io  173 
o.io  147 

O.IO  121 

o.io  095 

9-89  455 
9-89  445 
9-89  435 
9.89  425 
9.89  415 

10 
10 
10 
IO 

40 

39 
38 
37 
36 

j 

i 

i 

c 

>0 

50 

p 

)0 

5 
8 
ii 
H 

•7 
•5 
•3 

.2 

25 
26 
27 
28 
29 

9-79  335 
9-79  35i 
9-79  367 
9-79  383 
9-79  399 

16 

16 
16 
16 

9.89  931 

9-89  957 
9.89  983 
9.90009 
9-90  035 

26 
26 
26 
26 

o.io  069 
o.io  043 
o.io  017 

0.09  991 
0.09  965 

9.89  405 
9-89  395 
9-89  385 
9-89  375 
9.89  364 

xo 

IO 
10 

II 

35 
34 
33 
32 
3i 

6 

8 

I 
I 
I 

2 

5 
.6 

•9 
.1 

15 

1.5 

1.8 

2.0 

30 

3i 

32 
33 
34 

9-79  415 
9-79  431 
9-79  447 
9-79  463 
9-79  478 

16 
16 
16 
IS 

16 

9.90  06  1 
9.90  086 

9.90  112 
9.90  138 
9.90  164 

25 

26 
26 
26 
26 

0.09  939 
0.09  914 
0.09  888 
0.09  862 
0.09  836 

9-89  354 
9-89  344 
9-89  334 
9.89  324 
9.89  314 

IO 
10 
10 
10 

30 

29 

28 

27 

26 

9 

10 
20 

30 
40 
CO 

2 

2 

5 

8 

10 

70 

•4 
-7 
•3 

.0 

•7 

2-3 
2-5 

5-0 

7.5 

10.0 
12  ? 

!I 

37 
38 
39 

9.79  494 
9-79  51° 
9-79  526 
9-79  542 
9-79  558 

16 
16 
16 
16 

9.90  190 

9.90  216 

9.90  242 
9.90  268 

9.90  294 

26 
26 
26 
26 
tfi 

0.09  810 
0.09  784 
0.09  758 
0.09  732 
0.09  706 

9.89  304 
9.89  294 
9.89  284 
9.89  274 
9.89  264 

10 
10 
10 
IO 

25 
24 

23 

22 
21 

6 

i 

I 
I 

4O 

41 

4« 
43 
44 

9-79  573 
9-79  589 
9.79  605 
9.79  621 
9-79  636 

16 
16 
16 

»5 
tfi' 

9.90  320 
9.90  346 
9.90  371 

9.90  397 
9.90  423 

26 
25 
26 

26 
~f 

0.09  680 
0.09  654 
0.09  629 
0.09  603 
0.09  577 

9.89  254 
9.89  244 

9-89  233 
9.89  223 
9.89  213 

IO 
XI 
10 
10 

20 

19 

18 
17 
16 

7 

8 
9 

10 

20 
TO 

3 

C 

3 

7 
8 
7 

C 

45 
46 

47 
48 
49 

9-79  652 
9.79  668 

9-79  684 
9.79699 

9-79  715 

16 
16 

IS 

16 
tfi 

9.90  449 

9-90  475 
9.90  501 
9.90  527 
9-90  553 

26 
26 
26 
26 

0.09  551 
0.09  525 
0.09499 
0.09  473 
0.09  447 

9-89  203 
9.89  193 
9-89  183 
9.89  173 

9.89  162 

10 
10 

IO 

II 

15 
14 
13 

12 
II 

40 
50 

7 

9 

3 

2 

50 

51 

52 
53 
54 

9-79  731 
9-79  746 
9-79  762 
9-79  778 
9-79  793 

«5 

16 
•6 

15 

ifi 

9.90  578 
9.90604 
9.90  630 
9.90  656 
9.90  682 

25 
26 
26 
26 
26 
•>fi 

0.09  422 
0.09  396 
0.09  370 
0.09  344 
0.09  318 

9-89  152 
9.89  142 
9.89  132 

9.89  122 
9.89  112 

10 
10 
10 
10 

10 

9 
8 
7 
6 

6 

7 
8 

9 

IO 

0 
2 

3 

5 

7 

0-9 
I.I 
1.2 
1.4 
1.5 

55 
56 
57 
58 

.53- 

9-79  809 
9-79  825 
9.79  840 
9-79  856 
9-79  872 

16 
15 
16 
16 

9.90  708 
9-90  734 
99°  759 
9.90  785 
9.90  8ll 

26 
25 
26 
26 
ofi 

0.09  292 
0.09  266 
0.09  241 
0.09  215 
0.09  189 

9.89  ioi 

9.89  091 

9.89  081 
9.89  071 

(;.8<y  O')0 

10 
10 
10 

II 

5 
4 
3 

3 
I 

20 

3° 

40 
50 

3 
5 

6 

8 

3 

0 

7 
3 

3-o 
4-5 
6.0 

7-5 

00 

9-79  887 

J5 

9.«,o  837 

0.09  163 

9.89  050 

O 

L.  Cos. 

d. 

I,.  cotK. 

c.  d. 

L.TniiK. 

L.  Sin. 

d. 

r 

Pr 

op 

•' 

Ms. 

51' 


39C 


61 


r 

L.  Sin. 

d. 

L.Taug.  c.  d. 

L.  Cuts. 

L,.  Cos. 

d. 

Prop.  Pts. 

0 

1 

8 
9 

9-79  887 
9-79  9°3 
9-79  9i8 
9-79  934 
9-79  95° 

16 
15 
16 
16 
15 
16 
i5 
16 
15 
16 

15 
16 
15 
16 
15 
16 
15 
IS 
16 
iS 
16 
i5 
16 
15 

9.90  837 
9.90  863 
9.90  889 
9.90  914 
9.90  940 

26 
26 
25 
26 
26 
26 
26 

25 
26 
26 
26 
26 

25 
26 
26 
26 
26 
25 
26 
26 
26 
25 
26 
26 
26 

25 

26 
26 
26 
25 
26 
26 
26 
25 
26 

26 
26 
25 
26 
26 

25 
26 
26 
26 
25 
26 
26 
25 
26 
26 

25 
26 
26 
25 
26 

26 
25 
26 
26 
25 

0.09  163 
0.09  137 
0.09  in 
0.09  086 
0.09  060 

9.89  050 
9.89  040 
9.89  030 

9.89  020 
9.89  OO9 

10 
10 
10 

ii 

10 
IO 

II 

IO 

10 
10 

II 

10 

10 

II 

IO 
10 

II 

10 
IO 

II 

IO 
IO 

II 

10 

IO 

II 

10 

II 

10 
IO 

II 

10 

II 

IO 

II 

10 
10 

II 

IO 

II 

IO 

II 

10 

II 

10 

II 

10 

II 

IO 

II 

IO 

II 
II 

10 

6O 

59 

58 

57 

56 

6 

8 
9 

10 

20 

30 
40 
50 

6 

7 
8 

9 

10 
20 

3° 
40 

50 

6 

8 
9 

10 
20 

30 
40 

50 

6 
7 
8 
9 

10 

20 

3° 
40 

50 

6    i 

7    i 
8    I 

9    I 

IO     I 

20    3 

3°    5 
40    7 

50    9 

26 

2.6 

3-° 
3-5 
3-9 
4-3 
8-7 
13.0 

17-3 
21.7 

»5 

2-5 
2.9 

3-3 
3-8 
4.2 
8-3 
12.5 
16.7 

20.8 

16 
1.6 
1.9- 

2.1 
2.4 
2-7 
5-3 

8.0 
10.7 
13-3 

»5 

1-5 
1.8 

2.0 
2-3 
2-5 

5-0 

7.5 

IO.O 

12.5 

[I        10 

.1      I.O 
.3      1.2 

•5    1-3 
•7    i-5 
.8    1.7 
•7    3-3 

•5    5-0 
•3    6.7 

.2     8.3 

9-79965 
9.79981 

9-79  996 
9.80  012 
9.80  027 

9.90  966 
9.90  992 
9.91  018 
9.91  043 
9.91  069 

0.09  034 
0.09  008 
0.08  982 
0.08  957 
0.08  931 

9.88  999 
9.88  989 
9.88  978 
9.88  968 
9.88  958 

55 
54 
53 

52 
51 

10 

ii 

12 

lj 
11 

3 

19 

9.80*043 
9.80  058 
9.80  074 
9.80  089 
9.80  105 

9.91  095 

9.9!   121 
9.91   147 
9.91   172 
9.91   198 

0.08  905 
0.08  879 
0.08  853 
0.08  828 
0.08  802 

9.88  948 
9.88  937 
9.88  927 
9.88  917 
9.88  906 

50 

49 

48 

47 
46 

9.80  120 

9.80  136 
9.80  151 

9.80  166 
9.80  182 

9.91  224 
9.91  250 
9.91  276 
9.91  301 
9.91  327 

0.08  776 
0.08  750 
0.08  724 
0.08  699 
0.08  673 

9.88  896 
9.88  886 
9-88  875 
9.88  865 
9-88  855 

45 
44 
43 
42 
4i 

20 

21 
22 
23 
24     | 

9.80  197 
9.80  213 
9.80  228 
9.80  244 
9.80  259 

9-91  353 
9-91  379 
9.91  404 
9.91  430 
9.91  456 

0.08  647 
0.08  621 
0.08  596 
0.08  570 
0.08  544 

9.88  844 
9.88  834 
9.88  824 
9.88  813 
9.88  803 

40 

39 
38 

11 

25 
26 

27 
28 
29 

9.80  274 
9.80  290 
9.80  305 
9.80  320 
9.80  336 

16 
IS 
15 
16 

9.91  482 
9.91  507 
9-91  533 
9-9i  559 
9-91  585 

0.08  518 
0.08  493 
0.08  467 
0.08  441 
0.08  415 

9.88  793 
9.88  782 
9.88  772 
9.88  761 
9.88  751 

35 
34 
33 
32 
3i 

30 

3i 
32 
33 
34 
35 
36 
37 
38 
39 

9.80  351 
9.80  366 
9.80  382 
9.80  397 
9.80  412 

*5 
16 
IS 

15 

9.91  610 
9.91  636 
9.91  662 
9.91  688 
9.91  713 

0.08  390 
0.08  364 
0.08  338 
0.08  312 
0.08  287 

9.88  741 
9-88  730 
9.88  720 
9.88  709 
9.88  699 

30 

29 
28 
27 
26 

9.80  428 
9.80  443 
9.80  458 
9.80  473 
9.80  489 

15 
i5 
15 
16 

9-9i  739 
9.91  765 
9.91  791 
9.91  816 
9.91  842 

0.08  261 
0.08  235 
0.08  209 
0.08  184 
0.08  158 

9.88  688 
9.88  678 
9.88  668 
9.88  657 
9.88  647 

25 
24 

23 

22 
21 

40 

41 
42 

43 
44   | 

9.80  504 
9.80  519 
9-8o  534 
9.80  550 
9.80  565 

XS 
15 
15 
16 
15 
15 
15 
IS 
15 
16 

9.91  868 
9.91  893 
9.91  919 

9-9i  945 
9.91  971 

0.08  132 
0.08  107 
0.08  08  1 
0.08  055 
0.08  029 

9.88  636 
9.88  626 
9.88  615 
9.88  605 
9.88  594 

20 

19 

18 

17 

16 

45 
46 

47 

48 

49 

9.80  580 
9-8o  595 
9.80  610 
9.80  625 
9.80  641 

9.91  996 

9.92  022 
9.92  048 
9.92  073 
9.92  099 

0.08  004 
0.07  978 
0.07  952 
0.07  927 
0.07  901 

9.88  584 
9-88  573 
9-88  563 
9-88  552 
9-88  542 

15 
14 
13 

12 
II 

5O 

5i 
52 
53 
54  | 

9.80  656 
9.80  671 
9.80  686 
9.80  701 
9.80  716 

*5 
15 
15 
IS 
15 

9.92  125 
9.92  150 
9.92  176 
9.92  202 
9.92  227 

0.07  875 
0.07  850 
0.07  824 
0.07  798 
0.07  773 

9-88  531 
9.88  521 
9.88  510 
9.88  499 
9.88  489 

10 

9 

8 

7 
6 

55 
56 
57 
58 
59 

9.80  731 
9.80  746 
9.80  762 
9.80  777 
9.80  792 

JS 

'5 
16 
15 
15 
IS 

9-92  253 
9.92  279 
9.92  304 
9.92  330 
9-92  356 

0.07  747 
0.07  721 
0.07  696 
0.07  670 
0.07  644 

9.88  478 
9.88  468 
9.88  457 
9.88  447 
9-88  436 

10 

II 

10 

II 

5 
4 
3 

2 

I 

60   1 

9.80  807 

9-92  381 

0.07  619 

9-88  425 

0 

1  L.  Cos. 

d. 

L.  Cot&. 

C.  d. 

L.Tang. 

L.  Sin. 

d. 

r 

Prop.  Pts. 

50< 


62 


40° 


f 

L.  Sin. 

d. 

L.Tang. 

c.  d. 

L.Cotg. 

L.  Cos. 

d. 

Prop.  Pts. 

o 

I 

2 

3 

4 

9.80  807 
9.80  822 
9.80  837 
9.80  852 
9.80  867 

15 
15 
15 
15 
15 
15 
15 
15 
15 
15 
15 
15 
15 
is 
15 
15 
14 
15 
15 
15 
IS 

15 
15 
15 
14 
15 
15 
15 
15 
14 
15 
15 
15 

IS 
14 
IS 
IS 
14 
IS 

9.92  381 
9.92  407 
9-92  433 
9.92  458 
9.92  484 

26 
26 
25 
26 
26 

25 
26 
26 
25 
26 

25 
26 
26 
25 
26 

26 
25 
26 
25 
26 

26 
23 
26 
25 
26 

26 
25 
26 
25 
26 

25 
26 
26 
25 
26 

25 
26 
25 
26 
26 

25 
26 
25 
26 
25 
26 
25 
26 
26 
25 
26 
25 
26 
25 
26 

25 
26 
25 
96 
as 

0.07  619 

0.07  593 
0.07  567 
0.07  542 
0.07  516 

9.88  425 
9-88  415 
9.88  404 
9.88  394 
9-88  383 

10 

II 

10 

II 
II 

10 

II 
II 

IO 

II 
II 

IO 

II 
II 

10 

II 

II 

IO 

II 

II 
II 

10 

II 
II 
II 

10 

II 
II 
II 

IO 

II 
II 
II 
II 

60 

59 
58 
57 
56 

6 

7 

26 

2.6 

3-o 
3-5 
3-9 
4-3 
8-7 
13.0 

17-3 
21.7 

25 

2-5 
2.9 

3-3 
3-8 
4-2 
8-3 
12.5 
16.7 

20.8 

15 

i-5 
1.8 

2.0 
2-3 

2-5 

5-0 

7-5 

IO.O 

12.5 
14 

i-4 
1.6 
1.9 

2.1 

2.3 

4-7 
7.0 

9-3 
II-  7 

[I        10 
.1      I.O 
.3      1-2 

5    1-3 
•7    i.S 
.8    1.7 
•7    3-3 
•5    5-0 
•3    6.7 
.2    8.3 

5 
6 

7 
8 
9 

9.80  882 
9.80  897 
9.80  912 
9.80  927 
9.80  942 

9.92  510 
9-92  535 
9.92  561 
9.92  587 
9.92  612 

0.07  490 
0.07  465 
0.07  439 
0.07  413 
0.07  388 

9.88  372 
9.88  362 
9.88  351 
9.88  340 
9.88  330 

55 
54 
53 
52 
5i 

8 
9 

10 

20 
30 

10 

ii 

12 
13 
14 

9.80  957 
9.80  972 
9.80  987 

9.8l  002 
9.8l  017 

9.92  638 
9.92  663 
9.92  689 
9.92  715 
9.92  740 

0.07  362 
0.07  337 
0.07  311 
0.07  285 
0.07  260 

9.88  319 
9.88  308 
9.88  298 
9.88  287 
9.88  276 

50 

49 
48 
47 
46 

40 
So 

15 

16 
17 
18 

19 

9.8l  032 
9.8l  047 

9.81  061 
9.81  076 
9.81  091 

9.92  766 
9.92  792 
9.92  817 
9.92  843 
9.92  868 

0.07  234 
0.07  208 
0.07  183 
0.07  157 
0.07  132 

9.88  266 
9.88  255 
9.88  244 
9-88  234 
9.88  223 

45 
44 
43 
42 
41 

6 

7 
8 

9 

10 

20 

21 
22 
23 

24 

9.81  106 
9.81  121 
9.81  136 
9.81  151 
9.81  166 

9.92  894 
9.92  920 
9-92  945 
9.92  971 
9.92  996 

0.07  106 
0.07  080 
0.07  055 
0.07  029 
0.07  004 

9.88  212 
9.88  201 
9.88   191 

9.88  180 

9-88   169 

4O 

39 

38 
37 
36 

20 

3° 

40 
50 

6 

7 
8 

9 

10 

20 

30 
40 

50 

6 

7 
8 

9 

10 
20 
30 
40 

50 

6    i 
7    i 
8    I 

9    I 

10     I 

20     3 

30    5 
40    7 
50    9 

25 
26 
27 
28 
29 

9.81  180 
9.81  195 

9.8l  2IO 
9.8l  225 
9.8l  240 

9-93  022 
9.93  048 

9-93  °73 
9.93  099 
9-93  124 

0.06  978 
0.06  952 
0.06  927 
0.06  901 
0.06  876 

9-88  158 
9.88  148 
9.88  137 
9.88   126 
9.88   115 

35 
34 
33 
32 
3i 

30 

3i 

32 
33 

34 

9.8l  254 
9.8l  269 
9.8l  284 
9-81  299 
9.8l  314 

9-93  150 
9-93  175 
9-93  201 
9.93  227 
9-93  252 

0.06  850 
0.06  825 
0.06  799 
0.06  773 
0.06  748 

9.88  105 
9.88  094 
9.88  083 
9-88  072 

9.88  061 

30 

29 
28 
27 
26 

35 
36 
37 
38 
39 

9.8l  328 

9-  8  1  343 
9.81  358 
9.81  372 
9.81  387 

9.93  278 
9-93  303 
9-93  329 
9-93  354 
9-93  38o 

0.06  722 
0.06  697 
0.06  671 
0.06  646 
0.06  620 

9.88  051 
9.88  040 
9.88  029 
9.88  018 
9.88  007 

II 
II 
II 
II 

25 
24 
23 

22 

21 

40 

4i 
42 

43 
44 

9.81  402 
9.81  417 
9.81  431 
9.81  446 
9.81  461    , 

15 

14 
15 
IS 
14 
15 
15 
14 
15 

9-93  406 
9-93  43i 
9-93  457 
9.93  482 
9-93  5o8 

0.06  594 
0.06  569 
0.06  543 
0.06  518 
0.06  492 

9.87  996 
9.87  985 

9-87  975 
9.87  964 

9-87  953 

II 

10 

II 

20 

19 

18 
17 
16 

45 
46 
47 
48 
49 

9-8i  475 
9.81  490 
9-8i  505 
9.81  519 
9-8i  534 

9-93  533 
9-93  559 
9-93  584 
9.93  610 
9.93  636 

0.06  467 
0.06  441 
0.06  416 
0.06  390 
0.06  364 

9.87  942 
9.87  931 
9.87  920 
9.87  909 
9.87  898 

II 
II 
II 
II 

15 
14 
13 

12 
II 

50 

Si 

52 
53 
54 

9.81  549 
9-8i  563 
9.81  578 
9-8i  592 
9.81  607 

14 
15 
M 
15 

9-93  66  1 
9-93  687 
9-93  7" 
9-93  738 
9-93  763 

0.06  339 
0.06  313 
0.06  288 
0.06  262 
0.06  237 

9.87  887 
9.87  877 
9.87  866 
9-87  855 
9.87  844 

IO 

II 
II 
II 

10 

9 
8 

6 

P 

57 
58 
59 

9.81  622 
9.81  636 
9.81  651 
9.81  665 
9.81  680 

14 
IS 
»4 
15 

9-93  789 
9-93  814 
9-93  840 
9-93  865 
9-93  891 

0.06  211 

0.06  1  86 
0.06  160 
0.06  135 
0.06  109 

9-87  833 
9.87  822 
9.87  811 
9.87  800 
9.87  789 

II 
II 
II 
II 

5 
4 
3 

2 
I 

60 

9.81  694 

9-93  9i6 

0.06  084 

9.87  778 

0 

L.  Con.      d. 

L.  Cotg.  c.  d.  L.Tnng. 

L.  Sin.  |   d. 

/ 

Prop.  Pts. 

49' 


41 


/• 

L.  Sin. 

d. 

L.Tang.  c.  d. 

L.Cotg. 

It.  Cos. 

d. 

Prop.  Pts. 

o 

I 

2 

3 

4 

9.81  694 
9.81  709 
9.81  723 
9.81  738 
9.81  752 

15 
M 
15 
M 
15 
14 
15 
14 
15 
14 
15 
H 
14 
15 
14 
15 
14 
15 
*4 
14 
15 
14 
J4 
i5 
14 
14 
15 
M 
14 

9-93  9i6 
9-93  942 
9-93  967 
9-93  993 
9.94  018 

:: 

26 
25 
26 

25 
26 

25 
26 
25 
26 
25 
26 
25 
26 

25 
26 
25 
26 
25 
26 
25 

26 
25 
26 

25 
25 
26 
25 
26 

25 
26 
25 
26 
25 
26 
25 
25 
26 
25 
26 
25 
26 
25 
25 
26 
25 
26 
25 
26 

25 
25 
26 
25 
26 

25 
26 
25 
25 
26 

0.06  084 
0.06  058 
0.06  033 
0.06  007 
0.05  982 

9.87  778 
9.87  767 
9.87  756 
9-87  745 
9-87  734 

iz 
ii 
ii 
ii 
ii 
ii 
ii 
ii 
ii 
ii 
ii 
ii 
ii 
ii 
ii 

12 
II 
II 

« 

II 

II 
II 
II 
II 
12 
II 
II 
II 
II 
II 
12 
II 
II 
II 
II 
12 
II 
II 
II 
II 
12 
II 
II 
12 
II 
II 
II 
12 
II 
II 
12 
II 
II 
12 
II 
II 
12 
II 
II 
12 

6O 

59 
58 
57 
56 

6 
7 

26 

2.6 

3-o 
3-5 
3-9 
4-3 
8-7 
13.0 

17-3 
21.7 

«5 

2-5 
2.9 

3-3 
3-8 
4.2 
8-3 
12.5 
16.7 

20.8 

15 

i-5 
1.8 

2.0 

2-3 
2-5 

5-o 

7-5 

10.0 

12.5 

14 
1.4 

1.6 
1.9 

2.1 
2-3 

4-7 
7.0 

9-3 
11.7 

it   ii 

1.2  I.I 

1.4  1-3 
1.6  1.5 
1.8  1.7 

2.0   1.8 

*-o  3-7 
5-0  5-5 
3.0  7.3 
xo  9.2 

5 
6 

7 
8 
9 

9.81  767 
9.81  781 
9.81  796 
9.81  810 
9.81  825 

9.94  044 
9.94  069 

9-94  095 
9.94  120 
9.94  146 

0.05  956 
0.05  931 
0.05  905 
0.05  880 
0.05  854 

9.87  723 
9.87  712 
9.87  701 
9.87  690 
9.87  679 

55 
54 
53 
52 
Si 

8 
9 

10 

20 

3° 

10 

ii 

12 
13 
14 

9.81  839 
9.81  854 
9.81  868 
9.81  882 
9.81  897 

9-94  I7i 
9-94  197 
9.94  222 
9.94  248 
9-94  273 

0.05  829 
0.05  803 
0.05  778 
0.05  752 
0.05  727 

9.87  668 
9.87  657 
9.87  646 
9.87  635 
9.87  624 

50 

49 
48 

47 
46 

40 
50 

15 

16 

17 
18 

19 

9.81  911 
9.81  926 
9.81  940 
9-8i  955 
9.81  969 

9.94  299 
9-94  324 
9-94  350 
9-94  375 
9-94  4°* 

0.05  701 
0.05  676 
0.05  650 
0.05  625 

0.05  599 

9.87  613 
9.87  601 
9.87  59<> 
9-87  579 
9.87  568 

45 
44 
43 
42' 
4i 

•  6 

7 
8 

9 

10 

20 

21 
22 

23 
24 

9.81  983 
9.81  998 

9.82  012 
9.82  O26 
9.82  041 

9.94  426 
9-94  452 
9-94  477 
9-94  5°3 
9.94  528 

0.05  574 
0.05  548 
0.05  523 
0.05  497 
0.05  472 

9-87  557 
9.87  546 

9-87  535 
9.87  524 

9-87  513 

4O 

39 
38 
37 
36 

20 

30 

40 

50 

6 

7 
8 

9 

10 

20 

3° 
40 

50 

6 

7 
8 

9 

10 

20 

3° 

40 
50 

6 

7 
8 

9 

10 
20 
30 

4° 
50  i 

25 
26 

27 
28 

29 

9.82  055 
9.82  069 
9.82  084 
9.82  098 
9.82  112 

9-94  554 
9-94  579 
9.94  604 
9-94  630 
9-94  655 

0.05  446 
0.05  421 
0.05  396 
o-OS  370 
0-05  345 

9.87  501 
9.87  490 
9.87  479 
9.87  468 
9-87  457 

35 
34 
33 
32 
3i 

3O 

3i 

32 
33 
34 

9.82  126 
9.82  141 
9-82  155 
9.82  169 
9.82  184 

15 
14 
M 

15 

9.94  68  1 
9-94  7o6 
9-94  732 
9-94  757 
9-94  783 

0.05  319 
0.05  294 
0.05  268 
0.05  243 
0.05  217 

9.87  446 

9-87  434 
9.87  423 
9.87  412 
9.87  401 

3O 

29 
28 

27 
26 

35 
36 
37 
38 
39 

9.82  198 
9.82  212 
9.82  226 
9.82  240 
9.82  255 

H 
14 
J4 
i5 
M 
14 
H 
14 
15 
M 
*4 
14 
14 
H 
*4 
14 
15 
14 
14 
H 
14 
H 
H 
J4 
*4 

9.94  808 
9-94  834 
9-94  859 
9.94  884 
9-94  9io 

0.05  192 
0.05  166 
0.05  141 
0.05  116 
0.05  090 

9.87  390 
9.87  378 
9.87  367 
9-87  356 
9.87  345 

25 
24 
23 

22 
21 

40 

4i 
42 
43 
44 

9.82  269 
9.82  283 
9.82  297 
9.82  311 
9.82  326 

9-94  935 
9-94  961 
9.94  986 

9.95  OI2 

9-95  037 

0.05  065 
0.05  039 
0.05  014 
0.04  988 
0.04  963 

9-87  334 
9.87  322 
9.87311 
9.87  300 
9.87  288 

20 

19 

18 

17 
16 

45 
46 
47 
48 
49 

9.82  340 

9-82  354 
9.82  368 
9.82  382 
9.82  396 

9-95  062 
9.95  088 
9-95  "3 
9-95  139 
9-95  164 

0.04  938 
0.04  912 
0.04  887 
0.04  86  1 
0.04  836 

9.87  277 
9.87  266 

9-87  255 
9.87  243 
9.87  232 

15 
14 
J3 

12 
II 

50 

5i 
52 
53 
54 

9.82  410 
9.82  424 
9.82  439 

9-82  453 
9.82  467 

9.95  190 
9-95  215 
9-95  240 
9-95  266 
9-95  291 

0.04  8  10 
0.04  785 
0.04  760 
0.04  734 
0.04  709 

9.87  221 

9.87  209 

9.87  198 

9.87  187 
9-87  175 

10 

9 
8 
7 
6 

55 
56 
57 
58 
59 

9.82  481 
9.82  495 
9-82  509 
9.82  523 
9-82  537 

9-95  317 
9-95  342 
9-95  368 
9-95  393 
9-95  4i8 

0.04  683 
0.04  658 
0.04  632 
0.04  607 
0.04  582 

9.87  164 
9-87  153 
9.87  141 
9.87  130 
9.87  119 

5 
4 
3 

2 

I 

60 

9-82  55i 

9-95  444 

0.04  556 

9.87  107 

0 

JL.  Cos. 

d. 

L.  Cotg.  c.  d. 

L.Tang. 

L.  Sin. 

d. 

r 

Prop.  Pts. 

48C 


64 


42' 


/• 

L.  Sin. 

d. 

L.  Tang. 

c.  d.j  L.Cotg. 

L.  Cos.      d. 

Prop.  Pts. 

0 

I 

2 

3 
4 

9-82  551 
9.82  565 
9.82  579 
9-82  593 
9.82  607 

X4 
J4 
*4 
*4 

i4 
J4 
H 
'4 
14 
'4 

H 

*4 
14 
14 

9-95  444 
9-95  469 
9-95  495 
9-95  520 
9-95  545 

25 
26 
25 
25 
26 

25 
26 
25 
25 
26 

25 
25 
26 
25 
26 

25 
25 
26 
25 
26 

25 
25 
26 
25 
25 
26 
25 
26 
25 
25 
26 
25 
25 
26 
25 
25 
26 
25 
25 
26 

25 
26 
25 
25 
26 

25 
25 
26 
25 
25 
26 
25 
25 
26 
25 
25 
36 
25 
25 
26 

0.04  556 
0.04  531 
0.04  505 
0.04  480 
0.04  455 

9.87  107 
9.87  096 
9-87  085 
9.87  073 
9.87  062 

ii 
ii 

12 
II 
12 
II 
II 
12 
II 
12 
II 
12 
II 
12 
II 
12 
II 
II 
12 
II 
12 
12 
II 
12 
II 
12 
II 
12 
II 
12 
II 
12 
12 
II 
12 
II 
12 
12 
II 
12 
12 
II 
12 
12 
II 
12 
12 

12 
12 
12 
II 
12 
12 
II 
12 
12 
12 
II 
12 

60 

59 
58 
57 
56 

6 

8 
9 

10 
20 
30 
40 
50 

6 

8 
9 

10 
20 

30 
40 

50 

6 

7 
8 

9 

10 

20 
30 
40 

50 

6 
7 
8 

9 

10 

20 
30 
40 

50 

6 

7 
8 

9 

10 
20 
30 
40 

5°    * 

26 

2.6 

3-o 
3-5 
3-9 
4-3 
8-7 
13.0 

17-3 
21.7 

«5 

2-5 
2.9 

3-3 
3-8 
4-2 
8-3 
12.5 
16.7 

20.8 

14 

1.4 

1.6 

i-9 

2.1 
2-3 

4-7 
7.0 

9-3 
11.7 

13 
i-3 
i-S 
1-7 

2.0 
2.2 
4-3 
6-5 

8-7 
10.8 

ia      ii 

1.2     I.I 

1-4    1-3 
1.6    1.5 
1.8    1.7 

2.0     1.8 

4-0    3-7 
S.o    5-5 
B.o    7.3 
o.o    9.2 

5 
6 

7 
8 
9 

9.82  621 
9.82  635 
9.82  649 
9.82  663 
9.82  677 

9-95  571 
9-95  596 
9-95  622 
9-95  647 
9-95  672 

0.04  429 
0.04  404 
0.04  378 

0-04  353 
0.04  328 

9.87  050 
9.87  039 
9.87  028 
9.87  016 
9.87  005 

55 
54 
53 
52 
5i 

10 

ii 

12 
13 
14 

9.82  691 
9.82  705 
9.82  719 
9-82  733 
9.82  747 

9-95  698 
9-95  723 
9-95  748 
9-95  774 
9-95  799 

0.04  302 
0.04  277 
0.04  252 

0.04  226 

O.O4  2OI 

9-86  993 
9.86  982 
9.86  970 
9.86  959 
9-86  947 

50 

49 
48 
47 
46 

15 

16 

17 
18 

19 

9.82  761 
9.82  775 
9.82  788 
9.82  802 
9.82  816 

*4 
13 
14 
14 

9-95  825 
9-95  850 
9-95  875 
9-95  901 
9.95  926 

0.04  175 
0.04  150 
O.O4  125 
O.O4  099 
0.04  074 

9.86  936 
9.86  924 
9.86  913 
9.86  902 
9.86  890 

45 
44 
43 
42 
4i 

20 

21 
22 

23 
24 

9.82  830 
9.82  844 
9.82  858 
9.82  872 
9.82  885 

14 
14 
14 
13 
*4 
14 
14 
14 
14 
13 
14 
14 
14 
13 
14 
14 
14 
13 
14 
14 
H 
'3 
14 
14 
13 
14 
H 
13 
14 
13 
14 
M 
»3 
»4 
»3 
14 
»4 
'3 
»4 

9-95  952 
9-95  977 
9.96  002 
9.96  028 
9-96  053 

O.O4  048 
O.O4  O23 
0.03  998 
O.O3  972 

0.03  947 

9.86  879 
9.86  867 
9.86  855 
9.86  844 
9.86  832 

40 

39 
38 
37 
36 

25 
26 

27 
28 
29 

9.82  899 
9.82  913 
9.82  927 
9.82  941 
9-82  955 

9.96  078 
9.96  104 
9.96  129 

9-96  J55 
9.96  180 

0.03  922 
0.03  896 
0.03  871 
0.03  845 
0.03  820 

9.86  821 
9.86  809 
9.86  798 
9.86  786 
9.86  775 

35 

H 

32 
3i 

30 

31 
32 
33 

34 

9.82  968 
9.82  982 
9.82  996 
9.83  oio 
9.83  023 

9.96  205 
9.96  231 
9.96  256 
9.96  281 
9.96  307 

0.03  795 
0.03  769 
0.03  744 
0.03  719 
0.03  693 

9.86  763 
9.86  752 
9.86  740 
9.86  728 
9.86  717 

30 

29 
28 
27 
26 

35 
36 
37 
38 
39 

9-83  °37 
9.83  051 
9.83  065 
9.83  078 
9.83  092 

9.96  332 
9-96  357 
9-96  383 
9.96  408 

9-96  433 

0.03  668 
0.03  643 
0.03  617 
0.03  592 
0.03  567 

9.86  705 
9.86  694 
9.86  682 
9.86  670 
9.86  659 

25 
24 

23 

22 
21 

40 

4i 
42 
43 

44 

9.83  106 

9.83  120 

9-83  133 
9.83  147 

9.83  161 

9-96  459 
9.96  484 
9.96  510 

9-96  535 
9.96  560 

0.03  541 
0.03  516 
0.03  490 
0.03  465 
0.03  440 

9.86  647 
9.86  635 
9.86  624 
9.86  612 
9.86  600 

2O 

19 

18 

17 
16 

3 

47 
48 
49 

9-83  174 
9.83  188 

9.83  202 

9-83  215 
9.83  229 

9.96  586 
9.96  611 
9.96  636 
9.96  662 

9.96  687 

0.03  414 
0.03  389 
0.03  364 
0.03  338 
0.03  313 

9.86  589 
9.86  577 
9.86  565 
9-86  554 
9.86  542 

15 
14 
13 

12 
II 

5O 

5i 

52 
53 
54 

9.83  242 
9.83  256 
9.83  270 
9.83  283 
9.83  297 

9.96  712 
9.96  738 
9.96  763 
9.96  788 
9.96  814 

0.03  288 
0.03  262 
0.03  237 

0.03  212 

0.03  1  86 

9.86  530 
9.86  518 
9-86  507 
9.86  495 
9-86  483 

10 

9 

8 

7 
6 

55 
56 
57 
58 
59 

9.83  310 
9.83  324 
9.83  338 
9.83  351 
9.83  365 

9.96  839 
9.96  864 
9.96  800 
9.96  915 
9.96  940 

0.03  161 
0.03  136 
0.03  no 
0.03  085 
0.03  060 

9.86  472 
9.86  460 
9.86  448 
9.86  436 
9-86  425 

5 
4 
3 

2 
I 

00 

9.83  378 

13 

9.96  966 

0.03  034 

9-86  413 

0 

I,.  Cos.      d. 

L.  Cotg.  ,c.  d.  L.Tan^. 

I,.  Sin.   ;    <l. 

r 

Prop.  Pts. 

47' 


43< 


r 

L.  Sin. 

d. 

L.Tang 

c.  d 

L.  Cotg. 

L.  Cos. 

d. 

Prop.  Pts. 

O 

i 

2 

3 

4 

9-83  378 
9-83  392 
9-83  4°5 
9.83  419 
9-83  432 

14 
13 

*4 
*3 
J4 
13 
M 
T3 
14 
»3 
H 
13 
14 
13 
14 
13 
14 
13 
J3 
H 
13 
13 
H 
13 

9.96  966 
9.96  991 
9.97  016 
9.97  042 
9.97  067 

25 
25 
26 
25 
25 
26 
25 
25 
25 
26 

25 
25 
26 
25 
25 
26 
25 
25 
26 
25 
25 
26 
25 
25 
25 
26 
25 
25 
26 
25 

25 
26 
25 
25 
25 
26 
25 
25 
26 
25 

25 
26 
25 
25 
25 
26 
25 
25 
26 
25 
25 
25 
26 
25 
25 
26 
25 
25 
25 
26 

0.03  034 
0.03  009 

0.02  984 
O.O2  958 

0.02  933 

9.86  413 
9.86  401 
9.86  389 
9-86  377 
9.86  366 

12 
12 
12 
II 
12 
12 
12 
12 
12 
II 
12 
12 
12 
12 
12 
12 
12 
II 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 
12 

60 

59 
58 
57 
56 

6 

7 

36 

2.6 

3-o 
3-5 
3-9 
4-3 
8-7 
13-0 

17-3 
21.7 

25 

2-5 
2.9 

3-3 
3-8 
4.2 

8-3 
12.5 
16.7 

20.8 

14 

11 

i-9 

2.1 
2-3 

4-7 
7.0 

9-3 
H-7 

13 

i-3 
i.S 
1-7 

2.0 
2.2 

ti 

8.7 
10.8 

2         XI 

:.2    i.i 

f-4    i-3 
.6    1.5 
.8    1.7 

5.0      1.8 

k<>    3-7 
>-o    5-5 
•o    7-3 
>.o    9.2 

5 
6 

7 
8 

9 

9.83  446 
9-83  459 
9-83  473 
9.83  486 
9.83  500 

9-97  092 
9.97  118 
9-97  143 
9-97  168 
9-97  193 

0.02  908 
0.02  882 
0.02  857 
0.02  832 
0.02  807 

9-86  354 
9.86  342 
9.86  330 
9.86  318 
9.86  306 

55 
54 
53 
52 
5i 

8 
9 

10 
20 
30 

in 
ii 

12 
13 
14 

9-83  513 
9-83  527 
9-83  540 
9-83  554 
9-83  567 

9.97  219 
9-97  244 
9.97  269 
9-97  295 
9-97  320 

0.02  781 
0.02  756 
0.02  731 
0.02  705 
O.O2  680 

9.86  295 
9.86  283 
9.86  271 
9.86  259 
9.86  247 

50 

49 
48 
47 
46 

40 
50 

6 

8 
9 

10 
20 

3° 

£ 

6 

8 
9 

10 
20 

30 

40 

50 

6 
7 
8 

9 
10 

20 

30 
40 

50 
1 

6      ] 

7        3 

8      ] 

9      i 

10        S 

20      t 

30   d 

40      S 
50    ic 

15 

16 

17 
18 

19 

9-83  58i 
9-83  594 
9.83  608 
9.83  621 
9-83  634 

9-97  345 
9-97  371 
9-97  396 
9.97  421 
9-97  447 

0.02  655 
O.O2  629 
0.02  604 

0.02  579 
0.02  553 

9.86  235 
9.86  223 

9.86  211 
9.86  200 

9.86  188 

45 
44 
43 
42 
4i 

20 

21 
22 

23 
24 

9.83  648 
9.83  661 
9.83  674 
9.83  688 
9.83  701 

9.97  472 
9.97  497 
9-97  523 
9-97  548 
9-97  573 

0.02  528 
0.02  503 

0.02  477 

0.02  452 
0.02  427 

9.86  176 
9.86  164 
9.86  152 
9.86  140 
9.86  128 

40 

39 
38 

i 

25 
26 

27 
28 
29 

9-83  715 
9.83  728 
9.83  741 

9-83  755 
9.83  768 

J4 
13 
13 
H 
13 
*3 
H 
13 
13 
13 

9-97  598 
9-97  624 
9.97  649 
9-97  674 
9-97  700 

0.02  402 
O.O2  376 
0.02  351 
O.O2  326 
O.O2  300 

9.86  116 
9.86  104 
9.86  092 
9.86  080 
9.86  068 

35 
34 
33 
32 
3i 

30 

3i 
32 
33 
34 

9.83  781 
9-83  795 
9.83  808 
9.83  821 
9-83  834 

9-97  725 
9-97  750 
9-97  776 
9.97  801 
9.97  826 

0.02  275 
O.O2  250 
0.02  224 
O.O2  199 
0.02  174 

9.86  056 
9.86  044 
9.86  032 

9.86  020 
9.86  008 

30 

29 
28 

27 
26 

35 
36 
37 
38 
39 

9.83  848 
9.83  861 
9.83  874 
9.83  887 
9.83  901 

J4 
13 
13 
13 
H 

9-97  851 
9-97  877 
9.97  902 

9-97  927 
9-97  953 

O.O2  149 
0.02  123 
O.O2  098 
0.02  073 
0.02  047 

9.85  996 
9.85  984 
9.85  972 
9.85  960 
9.85  948 

25 
24 
23 

22 
21 

40 

4i 
42 
43 
44 

9.83  914 
9.83  927 
9.83  940 

9-83  954 
9.83  967 

J3 
13 
13 
14 
13 
*3 
13 
13 
I4 
13 
13 
13 
13 
13 
13 

9-97  978 
9.98  003 
9.98  029 
9.98  054 
9.98  079 

O.O2  O22 

o.oi  997 
o.oi  971 
o.oi  946 
o.oi  921 

9-85  936 
9.85  924 
9.85  912 
9-85  900 

9.85  888 

12 
12 
12 
12 

20 

19 
18 
17 
16 

45 
46 
47 
48 
49 

9.83  980 

9-83  993 
9.84  006 

9.84  020 
9-84  033 

9.98  104 
9.98  130 
9  98  155 
9.98  180 
9.98  206 

o.oi  896 
o.oi  870 
o.oi  845 
o.oi  820 
o.oi  794 

9.85  876 
9-85  864 
9-85  851 
9-85  839 
9-85  827 

12 

13 
12 
12 

IS 
14 
13 

12 
II 

50 

Si 

52 
53 

54 

9.84  046 
9.84  059 
9.84  072 
9.84  085 
9.84  098 

9.98  231 
9.98  256 
9.98  281 
9.98  307 
9-98  332 

o.oi  769 
o.oi  744 
o.oi  719 
o.oi  693 
o.oi  668 

9-85  815 
9-85  803 
9.85  791 
9.85  779 
9.85  766 

12 
12 
12 
13 

10 

9 
8 

6 

55 
56 
57 
58 
59 

9.84  112 
9.84  125 
9.84  138 
9.84  151 
9.84  164 

13 
13 
13 
13 

9-98  357 
9-98  383 
9.98  408 
9-98  433 
9.98  458 

o.oi  643 
o.oi  617 
o.oi  592 
o.oi  567 
o.oi  542 

9-85  754 
9.85  742 

9-85  730 
9.85  718 
9.85  706 

12 
12 
12 
12 

5 
4 
3 

2 
I 

60 

9.84  177 

9.98  484 

o.oi  516 

9-85  693 

X3 

0 

L.  Cos. 

d. 

L.  Cotg.  |c.  d. 

L.Tang. 

L.  Sin. 

d. 

/• 

Prop.  Pts. 

46C 


66 


44e 


/• 

I  .  Sin. 

d. 

L.Tang. 

c.  d. 

L.  Cotg. 

L.  Cos. 

d. 

Prop.  Pts. 

o 

I 

2 

3 
4 

9.84  177 
9.84  190 
9.84  203 
9.84  216 
9.84  229 

13 
13 
»3 
13 

9.98  484 
9.98  509 
9-98  534 
9  98  560 
9-98  585 

25 
25 
26 
25 
25 
25 
26 
25 
25 
26 

25 
25 
25 
26 
25 
25 
25 
26 
25 
25 
26 
25 
25 
25 
26 

25 
25 
25 
26 
25 

25 
26 
25 
25 
25 
26 
25 
25 
25 
26 

25 
25 
25 
26 
25 

25 
26 
25 
25 
25 
26 
25 
25 
25 
26 

25 
25 
25 
26 
25 

o.oi  516 
o.oi  491 
o.oi  466 
o.oi  440 
o.oi  415 

9-85  693 

9.85  681 

9.85  669 
9-85  657 
9.85  645 

12 
12 
12 
12 

GO 

59 
58 
57 
56 

6 
7 
8 

9 

10 
20 
30 
40 
50 

6 

7 
8 

9 

10 

20 

30 
40 

50 

6 

8 
9 

10 
20 

30 
40 
ero 

26 

2.6 

£ 

3-9 
4-3 
8-7 
13-0 
17-3 
21.7 

35 

2-5 
2.9 

3-3 
3-8 
4.2 
8-3 

w-S 

16.7 

20.8 

14 

1.4 

1.6 
1.9 

2.1 

2-3 

4-7 
7.0 

9-3 
11.7 

13 
i-3 
i-S 
i-7 

2.0 
2.2 

$ 

8-7 
10.8 

13 
1.2 
1.4 

1.6 
1.8 

2.0 
4.0 

6.0 
8.0 

10.0 

5 
6 

7 
8 

9 

9.84  242 

9-84  255 
9.84  269 
9.84  282 
9.84  295 

J3 
13 
14 
13 
13 
13 
13 
13 
13 
13 
13 

12 

13 
13 
13 

9.98  610 
9-98  635 
9.98  661 
9.98  686 
9.98  711 

o.oi  390 
o.oi  365 
o.oi  339 
o.oi  314 
o.oi  289 

9.85  632 

9.85  620 
9.85  608 

9-85  596 
9-85  583 

12 
12 
12 

13 

12 

12 
12 

13 
12 
12 

*3 

12 
12 

J3 

12 
12 

13 
12 
12 
13 
12 

13 
12 
12 

J3 

12 

13 
12 

13 
12 

12 

13 
12 

*3 

12 

J3 

12 

13 
12 

»3 
12 

13 
12 

13 
»3 
12 

13 
12 

»3 
12 

^3 
13 
12 

'3 
12 

55 
54 
53 
52 
5i 

10 

II 

12 
13 
14 

9.84  308 
9.84  321 
9-84  334 
9-84  347 
9.84  360 

9-98  737 
9.98  762 
9.98  787 
9.98  812 
9.98  838 

o.oi  263 
o.oi  238 
o.oi  213 
o.oi  188 
o.oi  162 

9-85  571 

9-85  559 
9-85  547 
9-85  534 
9.85  522 

50 

49 
48 

47 
46 

15 

16 
17 
18 

19 

9-84  373 
9-84  385 
9  84  398 
9.84411 
9  84  424 

9.98  863 
9.98  888 
9.98  913 
9-98  939 
9.98  964 

o.oi  137 

O.OI  112 

o.oi  087 
o.oi  061 
o.oi  036 

9-85  5io 
9-85  497 
9-85  485 
9-85  473 
9.85  460 

45 
44 
43 
42 

41 

20 

21 
22 

23 
24 

9-84  437 
9.84  450 
9.84  463 
9.84  476 
9.84  489 

J3 
13 
13 
13 
»3 

9.98  989 
9-99  oi5 
9  99  040 
9-99  065 
9.99  090 

O.OI  Oil 

o.oo  985 
o.oo  960 
o.oo  935 
o.oo  910 

9.85  448 
9-85  436 
9-85  423 
9.85  411 
9-85  399 

4O 

39 
38 
37 
36 

25 
26 
27 
28 
29 

9.84  502 

9-84  515 
9.84  528 
9.84  540 
9-84  553 

T3 
*3 
13 

12 

13 
13 
13 

J3 
13 
13 

12 

13 
13 
13 
13 
12 

13 
13 
13 
12 

13 
13 
*3 
12 
»3 
13 

13 
12 
13 
13 
12 

13 
13 
12 
13 
13 

9.99  116 

9-99  141 
9.99  166 

9  99  191 
9-99  217 

o.oo  884 
o.oo  859 
o.oo  834 
o.oo  809 
o.oo  783 

9.85  386 
9-85  374 
9-85  361 
9-85  349 
9-85  337 

35 
34 
33 
32 
3i 

30 

3i 
32 
33 
34 

9.84  566 

9-84  579 
9.84  592 
9-84  605 
9.84  618 

9.99  242 
9-99  267 
9-99  293 
9.99  318 

9-99  343 

o.oo  758 
o.oo  733 
o.oo  707 
o.oo  682 
o.oo  657 

9-85  324 
9-85  312 
9.85  299 
9-85  287 
9.85  274 

3O 

29 
28 
27 
26 

35 
36 
37 
38 
39 

9-84  630 

9-84  643 
9.84  656 
9.84  669 
9.84  682 

9.99  368 
9-99  394 
9-99  419 
9.99  444 

9-99  469 

o.oo  632 
o.oo  606 
o.oo  581 
o.oo  556 
o.oo  531 

9.85  262 
9.85  250 
9-85  237 
9.85  225 

9.85  212 

25 
24 

23 

22 
21 

6 

40 

4i 
42 
43 
44 

9.84  694 
9.84  707 
9.84  720 
9-84  733 
9-84  745 

9-99  495 
9-99  520 
9-99  545 
9-99  570 
9-99  596 

o.oo  505 
o.oo  480 
o.oo  455 
o.oo  430 
o.oo  404 

9.85  200 

9.85  187 

9-85  175 
9.85  162 
9.85  150 

20 

19 
18 

17 
16 

7 
8 

9 

10 

20 

3° 

45 
46 

47 
48 

49 

9.84  758 
9.84  771 
9.84  784 
9.84  796 
9.84  809 

9.99  621 
9-99  646 
9-99  672 
9-99  697 
9-99  722 

o.oo  379 
o.oo  354 
o.oo  328 
o.oo  303 
o.oo  278 

9-85  137 
9-85  125 

9-85  "2 

9.85  ioo 

9.85  087 

15 

H 
13 

12 
II 

40 
50 

6 

8 

9 
10 

5O 

5i 
52 
53 
54 

9.84  822 

9-84  835 
9.84  847 
9.84  860 
9.84  873 

9-99  747 
9-99  773 
9-99  798 
9-99  823 
9-99  848 

o.oo  253 
o.oo  227 

0.00  202 

o.oo  177 
o.oo  152 

9-85  074 
9.85  062 
9.85  049 
9-85  037 
9-85  024 

10 

9 
8 

6 

55 
56 
57 
58 

59 

9  84  885 
9.84  898 
9.84911 
9.84  923 
9.84  936 

9-99  874 
9-99  899 
9-99  924 
9-99  949 
9-99  975 

o.oo  126 

O.OO  IOI 

o.oo  076 
o.oo  051 
o.oo  025 

9.85  012 

9.84  999 
9.84  986 
9.84  974 
9.84  9°i 

5 
4 
3 

2 
I 

20 

30 
40 

50 

00 

9.84  9  jrv 

0.00  000 

O.OO  000 

9.84  949 

0 

L.  Cos. 

d. 

L.  Cot*. 

c.  d.  L.Tang. 

L.  Sin. 

d. 

f 

Prop.  Pts. 

45C 


o< 


TABLE  IV. 


r  r 

r 

s 

T 

0 

60 

120 
1  80 
240 

o 

i 

2 

3 
4 

4-68557 
.68557 
.68557 
.68557 
•68557 

4-68557 
-68557 
.68557 
.68557 
.68558 

300 
360 
420 
480 
540 

5 
6 

7 
8 

9 

4.68557 
.68557 
•68557 
•68557 
.68557 

4.68558 
.68558 
.68558 
.68558 
.68558 

600 
660 
720 
780 
840 

10 

ii 

12 
13 
14 

4-68557 
•68557 
.68557 
.68557 
.68557 

4-68558 
.68558 
.68558 
.68558 
.68558 

900 
960 
1020 
I080 
1140 

II 

17 

18 
19 

4-68557 
.68557 
.68557 
.68557 
.68557 

4-68558 
.68558 
.68558 
.68558 
•  .68558 

1200 
1260 
1320 
1380 
I440 

20 
21 
22 
23 

24 

4-68557 
.68557 
.68557 
.68557 
.68557 

4-68558 
.68558 
.68558 
.68558 
.68558 

1500 
1560 
1620 
1680 
1740 

25 
26 
27 
28 
29 

4-68557 
.68557 
•68557 
.68557 
.68557 

4-68558 
.68558 
.68558 
.68558 
•68559 

1800 

1860 
1920 
1980 
2040 

30 
31 
32 

33 

34 

4-68557. 
.68557 
.68557 
.68557 
-68557 

4-68559 
.68559 
.68559 
•68559 
•68559 

2100 
2160 
2220 
228O 
2340 

35 
36 
37 
38 
39 

4-68557 
.68557 
.68557 
.68557 
.68557 

4-68559 
.68559 
.68559 
.68559 
•68559 

2400 
2460 
2520 
2580 
2640 

40 
41 
42 

43 

44 

4-68557 
.68556 
.68556 
.68556 

.68556 

4-68559 
.68560 
.68560 
.68560 
.68560 

2700 
2760 
2820 
2880 
2940 

45 
46 

47 
48 
49 

4-68556 
.68556 
.68556 
.68556 
.68556 

4.68560 
.68560 
.68560 
.68560 
.68560 

3OOO 
3060 
3120 
3180 
3240 

50 

51 
52 
53 
54 

4.68556 
.68556 
.68556 
.68556 
.68556 

4.68561 
.68561 
.68561 
.68561 
.68561 

3300 
3360 
3420 
3480 
3540 

55 
56 
57 
58 
59 

4.68556 
.68556 
.68555 
.68555 
-68555 

4.68561 
.68561 
.6856! 
.68562 
.68562 

3600 

60 

4-68555 

4.68562 

r  r 

r 

S 

T 

3600 
3660 
3720 
3780 
3840 

0 

i 

2 

3 

4 

4.68555 
•68555 
•68555 
.68555 
•68555 

4.68562 
.68562 
.68562 
.68562 
.68563 

3900 
3960 
4020 
4080 
4140 

i 

7 
8 

9 

4.68555 
.68555 
.68555 
.68555 
.68555 

4.68563 
.68563 
.68563 
.68563 
.68563 

4200 
4260 
4320 
4380 
4440 

10 

ii 

12 
13 
14 

4-68554 
.68554 
.68554 
•68554 
•68554 

4.68563 
.68564 
.68564 
.68564 
.68564 

4500 
456o 
4620 
4680 
4740 

15 

16 

17 
18 

19 

4-68554 
.68554 
•68554 
.68554 
•68554 

4-68564 
.68565 
.68565 
.68565 
.68565 

4800 
4860 
4920 
4980 
5040 

20 
21 
22 

23 
24 

4.68554 
.68553 
.68553 
.68553 
•68553 

4-68565 
.68566 
.68566 
.68566 
.68566 

5100 
5160 
5220 
5280 
5340 

25 
26 

27 
28 
29 

4-68553 
•68553 
•68553 
•68553 
.68553 

4.68566 
.68567 
.68567 
.68567 
.68567 

5400 
546o 
5520 
558o 
5640 

30 
31 
32 

33 

34 

4-68553 
.68552 
.68552 
.68552 
.68552 

4-68567 
.68568 
.68568 
.68568 
.68568 

5700 
576o 
5820 
5880 
5940 

CO  CO  CO  CO  CO 
vO  OOvj  O\Cn 

4.68552 
.68552 
.68552 
.68552 
.68551 

4.68569 
.68569 
.68569 
.68569 
.68569 

6000 
6060 
6120 
6180 
6240 

40 

42 
43 
44 

4-68551 
.68551 
.68551 
.68551 
.68551 

4.68570 
.68570 
.68570 
.68570 
.68571 

6300 
6360 
6420 
6480 
6540 

45 
46 
47 
48 
49 

4-68551 
.68551 
.68550 
.68550 
.68550 

4.68571 
.68571 
.68572 
.68572 
.68572 

6600 
6660 
6720 
6780 
6840 

So 
51 

52 
53 

54 

4.68550 
.68550 
.68550 
.68550 
.68550 

4-68572 
.68573 
.68573 
.68573 
•68573 

6900 
6960 
7020 
7080 
7140 

55 
56 
57 
58 
59 

4.68549 
.68549 
.68549 
.68549 
.68549 

4.68574 
.68574 
.68574 
.68575 
.68575 

7200 

60 

4.68549 

4-68575 

Log  sin  a  =  log  a  "  -f  S. 


Log  tan  a  —  log  a  "  -j-  T. 


68 


r  r 

A 

S 

T 

7200 
7260 
7320 
7380 
7440 

o 

2 

3 
4 

4.68549 
.68549 
.68548 
.68548 
.68548 

4-68575 
•68575 
.68576 
.68576 
.68576 

7500 
7560 
7620 
7680 
7740 

5 
6 

7 
8 
9 

4.68548 
.68548 
.68548 
.68547 
.68547 

4.68577 
.68577 
.68577 
.68578 
.68578 

7800 
7860 
7920 
7980 
8040 

10 

ii 

12 
13 
14 

4.68547 
•68547 
.68547 
.68547 
.68546 

4.68578 
.68579 
•68579 
.68579 
.68579 

8100 
8160 
8220 
8280 
8340 

15 

16 
17 
18 
19 

4-68546 
.68546 
.68546 
.68546 
.68546 

4.68580 
.68580 
.68580 
.68581 
.68581 

8400 
8460 
8520 
8580 
8640 

20 
21 
22 

23 
24 

4-68545 
•68545 
•68545 
•68545 
.68545 

4.68582 
.68582 
.68582 
.68583 
.68583 

8700 
8760 
8820 
8880 
8940 

25 
26 
27 
28 
29 

4-68545 
•68544 
.68544 

.68544 
.68544 

4-68583 
.68584 
.68584 
.68584 
.68585 

9000 
9060 
9120 
9180 
9240 

30 
31 
32 

33 

34 

4.68544 
.68544 
•68543 
.68543 
.68543 

4.68585 
.68585 
.68586 
.68586 
.68587 

9300 
9360 
9420 
9480 
9540 

35 
36 
37 
38 
39 

4-68543 
•68543 
.68542 
.68542 
.68542 

4.68587 
.68587 
.68588 
.68588 
.68588 

9600 
9660 
9720 
9780 
9840 

40 
4i 
42 
43 
44 

4.68542 
.68542 
.68541 
.68541 
.68541 

4.68589 
.68589 
.68590 
•68590 
.68590 

9900 
9960 

10020 
I0080 
IOI40 

45 
46 
47 
48 
49 

4-68541 
.68541 
.68540 
.68540 
.68540 

4.68591 
.68591 
.68592 
.68592 
.68592 

10200 
10260 
10320 
10380 
10440 

50 
Si 
52 
53 
54 

4.68540 
.68540 
.68539 
•68539 
•68539 

4-68593 
•68593 
.68594 
.68594 
•68595 

10500 
10560 
I062O 
10680 
10740 

55 
56 
57 
58 
59 

4.68539 
.68539 
.68538 
.68538 
.68538 

4.68595 
•68595 
.68596 
.68596 

.68597 

10800 

60 

4.68538 

4.68597 

rr 

r 

S 

T 

10800 
10860 
10920 
10980 
11040 

0 

i 

2 

3 
4 

4-68538 
.68537 
•68537 
.68537 
.68537 

4.68597 
.68598 
.68598 
.68599 
.68599 

IIIOO 

11160 

1  1  220 
II280 
II340 

5 
6 

8 
9 

4-68537 
.68536 
.68536 
.68536 
.68536 

4.68599 
.68600 
.68600 
.68601 
.68601 

II400 

II460 
II520 
II580 
11640 

10 

ii 

12 
13 
14 

4-68535 
•68535 
.68535 
•68535 
•68534 

4.68602 
.68602 
.68603 
.68603 
.68604 

II7OO 
II760 
II820 
II880 
II940 

IS 

16 

17 
18 

19 

4-68534 
•68534 
.68534 
.68533 
-68533 

4.68604 
.68605 
.68605 
.68606 
.68606 

12000 
I2O6O 
I2I20 
I2I80 
12240 

20 
21 
22 

23 

24 

4-68533 
•68533 
.68532 
.68532 
•68532 

4.68607 
.68607 
.68608 
.68608 
.68609 

12300 
12360 
I242O 
12480 
12540 

25 
26 

27 
28 
29 

4-68532 
.68531 
.68531 
.68531 
.68531 

4.68609 
.68610 
.68610 
.68611 
.68611 

I26OO 
12660 
12720 
12780 
12840 

3Q, 
31 
32 

33 
34 

4.68530 
.68530 
.68530 
•68530 
.68529 

4.68612 
.68612 
.68613 
.68613 
.68614 

12900 
12960 
13020 
13080 
I3I40 

3 

37 
38 
39 

4.68529 
.68529 
.68529 
.68528 
.68528 

4.68614 
.68615 
.68615 
.68616 
.68616 

13200 
13260 
13320 
13380 
13440 

40 
4i 
42 
43 

44 

4.68528 
.68528 
.68527 
.68527 
.68527 

4.68617 
.68617 
.68618 
.68618 
.68619 

13500 
13560 
13620 
13680 
13740 

45 
46 
47 

48 

49 

4.68526 
.68526 
.68526 
.68526 
.68525 

4.68620 
.68620 
.68621 
.68621 
.68622 

13800 
13860 
13920 
13980 
14040 

50 
51 

52 
53 
54 

4-68525 
.68^25 
.68525 
.68524 
.68524 

4.68622 
.68623 
.68623 
.68624 
.68625 

I4IOO 
I4I60 
14220 
14280 
14340 

55 
56 
57 
58 
59 

4.68524 
.68523 
.68^23 
.68523 
.68522 

4.68625 
.68626 
.68626 
.68627 
.68628 

14400 

60 

4.68522 

4.68628 

Log  sin  a  =  log  a  "  -f  S. 


Log  tan  a  —  log  a  " 


TABLE   V. 


NATURAL 


SINES,  COSINES,  TANGENTS,  AND  COTANGENTS. 


o  / 

N.  Sin. 

N.  Tan. 

N.  Cot. 

N.  Cos. 

0   / 

N.  Sin. 

N.  Tan. 

N.  Cot. 

N.  Cos. 

0  o 

5 

10 

15 

20 

25 

.00  000 

145 
291 
436 
582 

727 

.00  OOO 

145 
291 
436 

582 

727 

Infinity. 
687.55 
343-77 
229.18 
171.89 
I37.5I 

Unity. 

•99  999 
998 
997 

90  o 

55 
5o 
45 
40 

35 

230 

35 

40 

45 
50 

55 

.04  362 
507 
653 
798 
.04  943 
.05  088 

.04  366 
512 
658 
803 
.04  949 
•05  095 

22.904 
22.164 
21.470 
20.819 
20.206 
19.627 

•99  905 
898 
892 
885 
878 
870 

87  30 
25 

20 

15 
10 

5 

30 

35 
40 

45 
So 
55 

.00  873 
.01  018 
164 
3°9 
454 
600 

.00873 

.01  018 
164 
309 

455 
600 

114-59 
98.218 
85.940 
76.390 
68.750 
62.499 

•99  996 
995 
993 
991 

989 
987 

3° 
25 

20 

15 
10 

5 

3  o 

5 

10 

15 

20 

25 

•05  234 
379 
524 
669 
814 
.05  960 

.05  241 
387 
533 
678 
824 
.05  970 

19.081 
18.564 
18.075 
17.611 
17.169 
16.750 

.99  863 
855 
847 
839 
831 
822 

87  o 

55 
So 
45 
40 

35 

1   0 

5 

10 

15 

20 
25 

•oi  745 
.01  891 

.02  036 

181 

327 

472 

.01  746 
.01  891 
.02  036 
182 
328 
473 

57.290 
52.882 
49.104 
45-829 
42.964 
40.436 

.99  985 
982 
979 
976 
973 
969 

89  o 

55 
So 
45 
40 

35 

30 

35 
40 

45 
So 

55 

.06  105 
250 
395 
540 
685 
831 

.06  116 
262 
408 

554 
700 
847 

16.350 
15.969 
.605 

15-257 
14.924 
.606 

.99  813 
804 

795 
786 
776 
766 

30 
25 
20 

15 

10 

5 

30 

35 
40 

45 
50 
55 

.02  618 
763 

.02  908 

•°3  °54 
199 

345 

.02  619 
764 

.02  910 

•03  055 
201 
346 

38.188 
36.178 
34.368 
32.730 
31.242 
29.882 

.99  966 
962 
958 
953 
949 
944 

3° 
25 

20 

15 
10 

5 

4  o 

5 

10 

15 

20 
25 

.06  976 

.07  121 
266 
411 

556 
701 

.06  993 
.07  139 
285 
43i 
578 
724 

14.301 
14.008 
13.727 
•457 
I3.I97 
12.947 

•99  756 
746 
736 
.  725 
714 
703 

86  o 

55 
50 
45 
40 

35 

2  o 

5 

10 

15 

20 
25 

.03  490 

635 
781 
.03  926 
.04  071 
217 

.03  492 
638 
783 
.03  929 

•04075 
220 

28.636 
27.490 
26.432 
25-452 
24.542 
23-695 

•99  939 
934 
929 
923 
917 
911 

88  o 

55 
50 
45 
40 

35 

30 

35 
40 

45 
So 

55 

.07  846 
.07  991 
.08  136 
281 
426 
571 

.07  870 
.08  017 
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25 

20 

15 
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5 

30 

35 
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25 
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298 
232 
167 

30 
25 

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5 

30 

35 
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45 
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374 
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27  o 
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•5647 
•5597 
•5547 
•5497 
.5448 

•84  339 
261 
182 
104 
.84  025 
.83  946 

30 
25 
20 

15 
10 

5 

28  o 

5 

10 

15 

20 
25 

.46  947 
•47  076 
204 
332 
460 
588 

•53  171 
358 
545 
732 
•53  920 
•54  107 

1.8807 

.8741 
.8676 
.8611 
.8546 
.8482 

.88  295 
226 
158 
089 
.88  020 
•87  951 

62  o 

55 
So 
45 
40 
35 

33  o 

5 

10 

15 

20 

25 

•54  464 
586 
708 
829 
•54  95i 
•55  072 

.64  941 
•65  148 
355 
563 
771 
.65  980 

1-5399 
•5350 
•5301 
•5253 
.5204 

.5156 

•83  867 
788 
708 
629 

549 
469 

67  o 

55 
5o 
45 
40 

35 

30 

35 
40 
45 
So 

55 

•47  7i6 

844 

•47  97i 
.48099 
226 
354 

•54  296 
484 

673 
.54  862 
•55  051 
241 

1.8418 

.8354 
.8291 
.8228 
.8165 
.8103 

.87  882 
812 
743 
673 
603 
532 

30 

25 

20 

15 
10 

5 

3° 
35 
40 

45 
50 

55 

•55  194 
3i5 
436 
557 
678 

799 

.66  189 
398 
608 
.66  818 
.67  028 
239 

1.5108 
.5061 

•5013 
.4966 
.4919 
•4872 

•83  389 
308 
228 

147 
.83066 
.82  985 

30 

25 

20 

15 
10 

5 

29  o 

5 

10 

IS 

20 

25 

.48  481 
608 

735 
862 
.48  989 
.49  116 

•55  43i 
621 
•55  812 
.56003 
194 
385 

1.8040 

•7979 
.7917 
.7856 
.7796 
•7735 

.87  462 

391 
321 
250 
178 
107 

61  o 

55 
So 
45 
40 

35 

34  o 

5 

10 

15 

20 

25 

•55  9*9 
.56  040 
160 
280 
401 
521 

•67  451 
663 

.67  875 
.68  088 
301 
514 

1.4826 
•4779 
•4733 
•4687 
.4641 
•4596 

.82  904 
822 
741 
659 
577 
495 

56  o 
55 
50 
45 
40 
35 

30 

35 
40 
45 
50 

55 

.49  242 
369 
495 
622 
748 
•49  874 

•56  577 
769 
.56962 
•57  155 
348 
54i 

1.7675 
•7615 
.7556 
.7496 
•7437 
•7379 

.87  036 
.86  964 
892 
820 
748 
675 

30 
25 
20 

IS 

10 

5 

30 

35 
40 

45 
So 
55 

641 
760 
.56  880 
.57000 
119 
238 

.68  728 
.68  942 
•69  157 
372 
588 
.69804 

1-4550 
.4505 
.4460 

.4415 
•4370 
.4326 

.82  413 
330 

248 

165 
.82  082 
.81  999 

30 

25 

20 

15 
10 

5 

30  o 

.50  ooo 

.57  735 

1.7321 

.86603 

60  o 

36  o 

•57  358 

.70  021 

1.4281 

.81  915 

55  o 

N.  Cos. 

N.  Cot. 

N.Tan. 

N.  Sin. 

o  / 

N.  Cos. 

N.  Cot. 

N.  Tan. 

N.  Sin. 

0   f 

73 


0   I 

N.  Sin. 

N.  Tan. 

N.  Cot. 

N.Cos. 

o  t 

N.  Sin. 

N.  Tan. 

N.Cot. 

N.Cos. 

35  o 

5 

10 

15 

2O 
25 

•57  358 
477 
596 
7iS 
833 
•57  952 

.70  021 
238 

455 
673 
.70  891 
.71  no 

1.4281 
•4237 
•4i93 
.4150 
.4106 
.4063 

.81  915 
832 
748 
664 
580 
496 

55  o 

55 
So 
45 
40 
35 

40  o 

5 

10 

15 

20 

25 

.64  279 
390 
501 
612 
723 
834 

.83  910 
•84  158 
407 
656 
.84  906 
•85  i57 

1.1918 
.1882 
.1847 
.1812 
.1778 
•1743 

.76  604 
5" 
4i7 
323 
229 

135 

50  o 

55 
So 
45 
4° 
35 

30 

35 
40 

45 
5o 
55 

.58  070 
189 
307 
425 
543 
66  1 

.71  329 

549 
769 
71  99p 

.72  211 
432 

1.4019 
•3976 
•3934 
.3891 
•3848 
.3806 

.81  412 
327 
242 
157 
.81  072 
.80  987 

30 
25 

20 

15 
10 

5 

30 

35 
40 
45 
50 
55 

.64  945 

•65  055 
166 
276 
386 
496 

.85  408 
660 
•85  912 
.86  166 
419 
674 

1.1708 
.1674 
.1640 
.1606 
•  1571 
•1538 

.76  041 
•75  946 

85J 
756 

661 
566 

30 
25 

20 

15 
10 

5 

36  o 

5 
10 

15 

20 
25 

•58  779 
.58  896 
.59014 

131 

248 

365 

.72  654 
.72  877 

•73  I00 

323 

547 
771 

1-3764 
•3722 
.3680 
•3638 
•3597 
•3555 

.80  902 
816 
730 

644 
558 
472 

54  o 

55 
So 
45 
40 
35 

41  o 

5 

10 

15 
20 

25 

.65  606 
716 

«  8^ 
•65  935 

.66  044 
153 

.86  929 
.87  184 
441 
698 

•87  955 
.88  214 

1.1504 
.1470 
.1436 
.1403 
.1369 
•1336 

•75  47i 
375 
280 

184 
•75  088 
-74  992 

49  o 

55 
So 
45 
40 
35 

30 

35 
40 

45 
50 

55 

.59  482 

599 
716 
832 
•59  949 
.60  065 

•73  996 

.74  221 

447 
674 
.74  900 
•75  128 

I-35H 
•3473 
•3432 
•3392 
•3351 
•33" 

.80  386 
299 

212 

125 
.80  038 

•79  95i 

30 
25 
20 

15 
10 

5 

30 
35 
40 

45 
50 

55 

.66  262 

37i 
480 
588 
697 
805 

.88  473 
732 
.88  992 
•89  253 
515 
.89  777 

1.1303 
.1270 
.1237 
.1204 
.1171 
•"39 

.74  896 
799 
703 
606 

509 
412 

30 

25 

20 

15 
IO 

5 

37  o 

5 

10 

15 
20 

25 

.60  182 
298 
414 
529 
645 
761 

•75  355 
584 
•75  812 
.76  042 
272 
502 

1.3270 
•3230 
.3190 

•3151 
.3111 
.3072 

.79  864 
776 
688 
600 
512 
424 

53  o 

55 
So 
45 
40 

35 

42  o 

5 

10 

15 

20 
25 

.66  913 

.67  021 

129 

237 

344 
452 

.90  040 
304 
569 
.90  834 
.91  099 
366 

1.1106 
.1074 
.1041 
.1009 
.0977 
•0945 

•74  314 
217 
1  20 

.74  022 

•73  924 

826 

48  o 

55 
50 
45 
40 
35 

30 
35 
40 

45 
50 
55 

876 
.60  991 
.61  107 

222 

337 

451 

•76  733 
.76964 

•77  I96 
428 
661 
•77  895 

1.3032 
•2993 

•2954 
•2915 
.2876 
.2838 

•79  335 
247 

Xf 
.79  069 

.78  980 
891 

30 
25 

20 

15 
10 

5 

3° 
35 
40 

45 
50 

55 

•67  559 
666 

773 
880 
.67  987 
.68093 

•91  633 
.91  901 
.92  170 
439 
709 
.92  980 

1.0913 
.0881 
.0850 
.0818 
.0786 
•0755 

.73  728 
629 
53i 
432 
333 
234 

30 

?5 

20 

IS 
10 

5 

38  o 

5 

10 

IS 

20 
25 

.61  566 

68  1 

795 
.61  909 
.62  024 
138 

.78  129 
363 
598 
•78  834 
.79  070 
306 

1.2799 
.2761 
•2723 
•2685 
.2647 
.2609 

.78  801 
711 
622 
532 
442 
35i 

52  o 
55 
So 
45 
40 

35 

43  o 

5 

10 

15 

20 
25 

.68  200 
306 
412 
5i8 
624 
730 

•93  252 
524 
•93  797 
•94  071 
345 
620 

1.0724 
.0692 
.0661 
.0630 

•0599 
•0569 

•73  135 
•73  036 
.72  937 
837 
737 
637 

47  o 

55 
So 
45 
40 

35 

30 

35 
40 

45 
50 

55 

.62  251 
365 
479 
592 
706 
819 

•79  544 
•79  78i 

.80  020 
258 
498 
738 

1.2572 

•2534 
.2497 
.2460 
.2423 
.2386 

.78  261 
170 
.78  079 
•77  988 
897 
806 

30 
25 

20 

15 
10 

5 

30 

35 
40 
45 
5o 

55 

.68  835 
.68  941 
.69  046 
I5i 
256 
361 

.94  896 
•95  173 
451 
•95  729 
.96008 
288 

1.0538 
.0507 
.0477 
.0446 
.0416 
•0385 

•72  537 
437 
337 
236 
136 
•72  035 

30 
25 

20 

15 
10 

5 

39  o 

5 

10 

15 

20 
25 

.62  932 
•63  045 
158 
271 

383 
496 

.80  978 
.81  220 
46l 
703 
.81  946 
.82  igO 

1.2349 
.2312 
.2276 
•2239 
.2203 
.2167 

•77  715 
623 

531 
439 
347 
255 

51  o 

55 
So 
45 
40 
35 

44  o 

5 

10 

15 

20 

25 

.69  466 
570 
675 
779 
883 
.69  987 

.96  569 
.96  850 

•97  133 
416 
700 
•97  984 

1-0355 
•0325 
.0295 
.0265 
•0235 
.0206 

•7i  934 
833 
732 
630 

529 
427 

46  o 

55 
5o 
45 
40 
35 

30 

35 
40 

45 
50 

55 

.63  608 
720 
832 
.63  944 
.64  056 
167 

.82  434 
678 
.82  923 
.83  169 

415 
662 

1.2131 
•2095 
.2059 
.2024 
.1988 
•1953 

.77  162 
.77  070 
.76  977 
884 
791 
698 

30 
25 

20 

15 
10 

5 

30 

35 
40 

45 
So 

55 

.70  091 

195 
298 
401 

505 
608 

.98  270 
556 
•98  843 
•99  131 
420 
•99  7io 

1.0176 
.0147 
.0117 
.0088 
.0058 
.0029 

•71  325 
223 

121 
.71  019 
.70  916 
813 

30 
25 
20 

IS 

10 

5 

40  o 

.64  279 

.83  910 

1.1918 

.76  604 

50  o 

45  o 

.70  711 

1.  00  000 

1.  0000 

.707" 

45  o 

N.Cos. 

N.  Cot 

N.  Tan. 

N.  Sin. 

o  / 

N.  Cos. 

N.  Cot. 

N.  Tan. 

N.  Sin. 

o  / 

74        TABLE  VI. — CIRCULAR  ARCS  EXPRESSED  IN  RADIANS. 


DEGREES. 

MINUTES. 

SI  <  OM>S. 

o° 

I 

2 

3 
4 

I 

7 
8 

9 
10 

ii 

12 
13 
14 
15 

16 

17 

18 

19 
20 

21 
22 
33 
24 
25 
26 

27 

28 
29 

30 

3i 

32 
33 
34 

35 
36 

37 
38 
39 
40 

4i 
42 
43 
44 
45 
46 

47 
48 

49 
50 

Si 
52 

53 
54 

3 

57 
58 
59 
<i(> 

o.ooooo  oo 

60° 

61 
62 
63 
64 

65 
66 

67 
68 
69 
70 

71 
72 

73 
74 
75 
76 

77 
78 
79 
80 
81 
82 
83 
84 
85 
86 

87 
88 
89 
90 

9i 
92 

93 
94 
95 
96 

97 
98 
99 
10O 

101 
IO2 
103 
104 

IOI 

106 
107 
108 
109 
110 
in 

112 

"3 
"4 
"5 
116 

H7 
118 
119 
120 

1.04719  76 

120° 

121 
122 
123 
I24 

125 

126 

127 
128 
129 

130 

131 
132 
133 
134 
135 
136 

137 
138 
139 
140 
141 
142 
143 
144 

I4I 

146 

147 
148 

149 
150 

151 
152 
153 
154 
155 
156 

157 
158 
159 
160 
161 
162 
163 
164 
165 
166 

167 
168 
169 
170 

171 
172 
173 
174 
175 
I76 

177 
178 
179 
1HO 

2.09439  51 

O' 

I 

2 

3 
4 
5 
6 

7 

8 

9 
10 

ii 

12 
13 
14 
IS 

16 

17 
18 
19 
20 

21 
22 

23 
24 

25 
26 

27 
28 
29 

30 

3i 

32 
33 

34 

11 

37 
38 
39 
40 

4i 
42 

43 
44 
45 
46 

47 
48 
49 
50 

51 
52 
53 
54 
55 
56 
57 
58 
59 
00 

0.00000  00 

O" 

I 

2 

3 
4 

6 

7 
8 

9 
10 

ii 

12 
13 
14 
15 

16 

17 
18 

19 
20 

21 
22 
23 

24 

3 

27 
28 
29 
30 

3i 
32 
33 
34 
35 
36 

37 
38 
39 
40 

4i 
42 

43 
44 
45 
46 

47 
48 
49 
50 

51 
52 
53 
54 
55 
56 
57 
58 
59 
(10 

o.ooooo  oo 

0.01745  33 
0.03490  66 
0.05235  99 
0.06981  32 
0.08726  65 
0.10471  98 
0.12217  3° 
0.13962  63 
0.15707  96 

1.06465  08 
1.08210  41 
i  -°9955  74 
1.11701  07 
1.13446  40 
1.15191  73 
1.16937  06 
1.18682  39 
1.20427  72 

2.11184  84 
2.12930  17 
2.14675  50 
2.16420  83 
2.18166  16 
2.19911  49 
2.21656  82 
2.23402  14 
2.25147  47 

0.00029  °9 
0.00058  I  8 
0.00087  27 
0.00116  36 
0.00145  44 
0.00174  53 
0.00203  62 
0.00232  71 
0.00261  80 

o.ooooo  48 
o.ooooo  97 
o.ooooi  45 
o.ooooi  94 

O.OOOO2  42 
0.00002  91 

0.00003  39 
0.00003  88 
0.00004  36 

0.17453  29 

1.22173  °5 

2.26892  80 

0.00290  89 

0.00004  85 

0.19198  62 
0.20943  95 
0.22689  28 
0.24434  61 
0.26179  94 
0.27925  27 
0.29670  60 
0.31415  93 
0.33161  26 

1.23918  38 
1.25663  71 
1.27409  04 
1.29154  36 
1.30899  69 

1.32645  02 

1-3439°  35 
1.36135  68 
1.37881  01 

2.28638  13 
2.30383  46 
2.32128  79 
2.33874  12 
2.35619  45 
2.37364  78 
2.39110  ii 
2.40855  44 
2.42600  77 

0.00319  98 
0.00349  07 
0.00378  15 
0.00407  24 
0.00436  33 
0.00465  42 
0.00494  51 
0.00523  60 
0.00552  69 

0.00005  33 
0.00005  82 
0.00006  30 
0.00006  79 
0.00007  27 
0.00007  76 
0.00008  24 
0.00008  73 
0.00009  2I 

0.34906  59 

1.39626  34 

2.44346  10 

0.00581  78 

0.00009  7° 

0.36651  91 
0.38397  24 
0.40142  57 

0.41887  90 
0.43633  23 
0.45378  56 
0.47123  89 

0.48869  22 

0.50614  55 

1.41371  67 
1.43117  oo 
1.44862  33 
1.46607  66 
1.48352  99 
1.50098  32 
1.51843  64 
1-53588  97 
1-55334  30 

2.46091  42 
2.47836  75 
2.49582  08 
2.51327  41 
2.53072  74 
2.54818  07 

2.56563  40 
2-58308  73 
2.60054  06 

0.00610  87 
0.00639  95 
0.00669  °4 
0.00698  13 

0.00727  22 
0.00756  31 
0.00785  40 

0.00814  49 
0.00843  S8 

o.oooio  18 
o.oooio  67 
o.oooii  15 
o.ooon  64 

0.00012  12 
O.OOOI2  6l 

0.00013  09 
0.00013  57 
0.00014  06 

0.52359  88 

1.57079  63 

2.61799  39 

0.00872  66 

0.00014  54 

0.54105  21 

0.55850  54 
0-57595  87 
0.59341  19 
0.61086  52 
0.62831  85 
0.64577  1  8 
0.66322  51 
0.68067  84 

1.58824  96 
1.60570  29 
1.62315  62 
1.64060  95 
1.65806  28 
1.67551  61 
1.69296  94 
1.71042  27 
1.72787  60 

2.63544  72 
2.65290  05 
2.67035  38 
2.68780  70 
2.70526  03 
2.72271  36 
2.74016  69 

2.75762  02 

2.77507  35 

0.00901  75 
0.00930  84 
0.00959  93 
0.00989  02 
0.01018  ii 

0.01047  20 
0.01076  29 
O.OII05  38 
O.OII34  46 

0.00015  °3 
0.00015  5i 
0.00016  oo 
0.00016  48 
0.00016  97 
0.00017  45 
0.00017  94 
0.00018  42 
0.00018  91 

0.69813  17 

1.74532  93 

2.79252  68 

0.01163  55 

0.00019  39 

0.71558  50 
0.73303  83 
0.75049  16 

0.76794  49 
0.78539  82 
0.80285  15 
0.82030  47 
0.83775  80 
0.85521  13 

1.76278  25 
1.78023  58 
1.79768  91 
1.81514  24 

1-83259  57 
1.85004  90 

1.86750  23 
1.88495  56 
1.90240  89 

2.80998  01 
2.82743  34 
2.84488  67 
2.86234  oo 

2.87979  33 
2.89724  66 

2.91469  99 
2.93215  31 
2.94960  64 

0.01192  64 
0.01221  73 
0.01250  82 
0.01279  91 
0.01309  oo 
0.01338  09 
0.01367  17 

0.01396  26 
0.01425  35 

0.00019  88 

0.00020  36 
0.00020  85 

0.00021  33 

0.00021  82 
0.00022  30 

0.00022  79 
0.00023  27 
0.00023  76 

0.87266  46 

1.91986  22 

2.96705  97 

0.01454  44 

0.00024  24 

0.89011  79 
0.90757  12 
0.92502  45 
0.94247  78 

0-95993  « 
0.97738  44 

0.99483  77 
1.01229  I0 
1.02974  43 

I-9373I  55 
1.95476  88 

1.97222  21 

1.98967  53 
2.00712  86 
2.02458  19 
2.04203  52 
2.05948  85 
2.07694  1  8 

2.98451  30 
3.00196  63 
3.01941  96 
3.03687  29 
3.05432  62 
3.07177  95 
3.08923  28 
3.10668  61 
3.12413  94 

0.01483  53 
0.01512  62 
0.01541  71 
0.01570  80 
0.01599  89 
0.01628  97 
0.01658  06 
0.01687  15 
0.01716  24 

0.00024  73 

0.00025  21 

0.00025  70 
0.00026  1  8 
0.00026  66 
0.00027  15 
0.00027  63 

0.00028  12 

0.00028  60 

1.04719  76 

2.09431)  M 

3.14159  27 

3.01745  ; 

0.00029  09 

TABLE  VII. 
NAPIERIAN  LOGARITHMS  OF  NUMBERS. 


75 


N. 

Log. 

N. 

Log. 

N. 

Log. 

N. 

Log. 

N. 

Log. 

i 

2 

3 

4 
5 

0.00000 

0.69315 

1.09861 

1.38629 
1.60944 

21 
22 
23 
24 
25 

3-04452 
3.09104 

3-13549 
3-17805 
3.21888 

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UNIVERSITY  OF  CALIFORNIA  LIBRARY 
BERKELEY 

Return  to  desk  from  which  borrowed. 
This  book  is  DUE  on  the  last  date  stamped  below. 


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